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- Biblioteca Digitais de Teses e Dissertações da USP
- Universidade Rice
- Universidade Carlos III de Madrid
- Blackwell
- Oxford University Press
- The Berkeley Electronic Press
- The American Physical Society
- Institute of Physics
- Birkbeck, University of London, School of Economics, Mathematics and Statistics
- Elsevier
- Universidade Cornell
- Applied Probability Trust
- Hindawi Publishing Corporation
- London School of Economics and Political Science Thesis
- Sociedad Mexicana de Física
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## CALFRAC: Programa que quantifica o processo de cristalização fracionada e sua aplicação ao estudo de soleiras da Bacia do Paraná (Estado do Paraná); CALFRAC: Program to quantify fractional crystallization processes and your application in the study Paraná Basin sills (Paraná).

Fonte: Biblioteca Digitais de Teses e Dissertações da USP
Publicador: Biblioteca Digitais de Teses e Dissertações da USP

Tipo: Dissertação de Mestrado
Formato: application/pdf

Publicado em 06/12/2010
Português

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#Análise por ativação neutrônica#Computer program#Cristalização fracionada#Fractional Crystallization#Major and minor element modeling#Modelagem de elementos maiores e menores#Modelagem de elementos traços#Neutron activation analysis#Paraná Magmatic Province#Programa computacional#Província Magmática do Paraná

Foi desenvolvido um programa computacional escrito na linguagem de programação C++ denominado CALFRAC para quantificar o processo de cristalização fracionada em sistemas ígneos, utilizando para isso as concentrações dos elementos maiores, menores e traços. O algoritmo moderniza, torna mais eficiente e aprimora os programas publicados na literatura e possui a grande vantagem de poder calcular, automaticamente, todas as possíveis combinações de evolução das amostras envolvidas na diferenciação, além de associar aos cálculos os elementos-traço, os quais servem para confirmar os resultados sugeridos pelos ajustes dos elementos maiores e menores. O CALFRAC calcula a fração total subtraída do magma inicial e as frações referentes a cada mineral fracionado através do cálculo do balanço de massa, utilizando as concentrações de elementos maiores e menores, empregando os métodos de estimativa de máxima verossimilhança e dos multiplicadores de Lagrange para a resolução por mínimos quadrados, enquanto para os elementos-traço o programa utiliza a Equação de Rayleigh. Em ambos os casos a média dos erros percentuais relativos é usada como indicação das melhores evoluções. O programa CALFRAC foi aplicado na investigação da possibilidade de diferenciação por cristalização fracionada em amostras de soleiras de diabásio da Bacia do Paraná...

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## Fast, Exact Synthesis of Gaussian and nonGaussian Long-Range-Dependent Processes

Fonte: Universidade Rice
Publicador: Universidade Rice

Tipo: Relatório

Português

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Originally submitted to IEEE Transactions on Information Theory, August 1999.; 1/f noise and statistically self-similar random processes such as fractional Brownian motion (fBm) and
fractional Gaussian noise (fGn) are fundamental models for a host of real-world phenomena, from network
traffic to DNA to the stock market. Synthesis algorithms play a key role by providing the feedstock
of data necessary for running complex simulations and accurately evaluating analysis techniques. Unfortunately,
current algorithms to correctly synthesize these long-range dependent (LRD) processes are
either abstruse or prohibitively costly, which has spurred the wide use of inexact approximations. To fill
the gap, we develop a simple, fast (O(N logN) operations for a length-N signal) framework for exactly
synthesizing a range of Gaussian and nonGaussian LRD processes. As a bonus, we introduce and study
a new bi-scaling fBm process featuring a "kinked" correlation function that exhibits distinct scaling laws
at coarse and fine scales.

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## Wald Tests of I(1) against I(d) alternatives : some new properties and an extension to processes with trending components

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em 25/06/2007
Português

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This paper analyses the power properties, under fixed alternatives, of a Wald-type test, i.e., the (Efficient) Fractional Dickey-Fuller (EFDF) test of I(1) against I(d), d<1, relative to LM tests. Further, it extends the implementation of the EFDF test to the presence of deterministic trending components in the DGP. Tests of these hypotheses are important in many macroeconomic applications where it is crucial to distinguish between permanent and transitory shocks because shocks die out in I(d) processes with d<1. We show how simple is the implementation of the EFDF in these situations and argue that, under fixed alternatives, it has better power properties than LM tests. Finally, an empirical application is provided where the EFDF approach allowing for deterministic components is used to test for long-memory in the GDP p.c. of several OECD countries, an issue that has important consequences to discriminate between alternative growth theories.

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## Simple Wald tests of the fractional integration parameter : an overview of new results

Fonte: Universidade Carlos III de Madrid
Publicador: Universidade Carlos III de Madrid

Tipo: Trabalho em Andamento
Formato: application/pdf

Publicado em /01/2008
Português

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This paper presents an overview of some new results regarding an easily implementable Wald test-statistic (EFDF test) of the null hypotheses that a time-series process is I(1) or I(0) against fractional I(d) alternatives, with d∈(0,1), allowing for unknown deterministic components and serial correlation in the error term. Specifically, we argue that the EFDF test has better power properties under fixed alternatives than other available tests for fractional roots, as well as analyze how to implement this test when the deterministic components or the long-memory parameter are subject to structural breaks.

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## A fractional Dickey-Fuller test for unit roots

Fonte: Blackwell
Publicador: Blackwell

Tipo: Artigo de Revista Científica
Formato: application/pdf; text/plain

Publicado em /09/2002
Português

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This paper presents a new test for fractionally integrated (FI) processes. In particular, it proposes a testing procedure in the time domain that extends the well-known Dickey-Fuller approach. Monte-Carlo simulations support the analytical results derived in the paper and show that proposed tests fare very well, both in terms of power and size, when compared with others available in the literature. The paper ends with two empirical applications.

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## Simple wald tests of the fractional integration parameter: an overview of new results

Fonte: Oxford University Press
Publicador: Oxford University Press

Tipo: Parte de Livro
Formato: application/pdf

Publicado em //2009
Português

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This paper presents an overview of some new results regarding an easily implementable Wald test-statistic (EFDF test) of the null hypotheses that a time-series process is I(1) or I(0) against fractional I(d) alternatives, with d ∈ (0, 1), allowing for unknown deterministic components and serial correlation in the error term. Specifically, we argue that the EFDF test has better power properties under fixed alternatives than other available tests for fractional integration, as well as analyze how to implement this test when the determinitic components or the long-memory parameter are subject to structural breaks.; Forthcoming 2008

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## Wald Tests of I(1) against I(d) alternatives: some new properties and an extension to processes with trending components

Fonte: The Berkeley Electronic Press
Publicador: The Berkeley Electronic Press

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em //2008
Português

Relevância na Pesquisa

46.01%

This paper analyses the behaviour of a Wald-type test, i.e., the (E¢ cient) Fractional
Dickey-Fuller (EFDF) test of I(1) against I(d); d < 1; relative to LM tests. Further, it extends
the implementation of the EFDF test to the presence of deterministic trending components in
the DGP. Tests of these hypotheses are important in many macroeconomic applications where
it is crucial to distinguish between permanent and transitory shocks because shocks die out in
I(d) processes with d < 1. We show how simple is the implementation of the EFDF in these
situations and argue that, under xed alternatives, it is preferred to the LM test in Bahadur´ s
sense. Finally, an empirical application is provided where the EFDF approach allowing for
deterministic components is used to test for long-memory in the GDP p.c. of several OECD
countries, an issue that has important consequences to discriminate between alternative growth
theories.; Forthcoming 2008

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## The Periodogram of fractional processes

Fonte: Blackwell
Publicador: Blackwell

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em //2007
Português

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#Discrete Fourier transform#Long-range dependence#Long memory#Nonstationary series#Log-periodogram regression#Asymptotic normality#Primary: 62M15#Secondary: 62M10, 60G18#Economía

We analyse asymptotic properties of the discrete Fourier transform and the periodogram of time series obtained through (truncated) linear filtering of stationary processes. The class of filters contains the fractional differencing operator and its coefficients decay at an algebraic rate, implying long-range-dependent properties for the filtered processes when the degree of integration α is positive. These include fractional time series which are nonstationary for any value of the memory parameter (α ≠ 0) and possibly nonstationary trending (α ≥ 0.5). We consider both fractional differencing or integration of weakly dependent and long-memory stationary time series. The results obtained for the moments of the Fourier transform and the periodogram at Fourier frequencies in a degenerating band around the origin are weaker compared with the stationary nontruncated case for α > 0, but sufficient for the analysis of parametric and semiparametric memory estimates. They are applied to the study of the properties of the log-periodogram regression estimate of the memory parameter α for Gaussian processes, for which asymptotic normality could not be showed using previous results. However, only consistency can be showed for the trending cases...

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## Efficient wald tests for fractional unit roots

Fonte: Blackwell
Publicador: Blackwell

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em /03/2007
Português

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#Long memory#Serial correlation#Dickey–Fuller test#Lagrange multiplier test#Fractional processes#Local power#Economía

In this article we introduce efficient Wald tests for testing the null hypothesis of the unit root against the alternative of the fractional unit root. In a local alternative framework, the proposed tests are locally asymptotically equivalent to the optimal Robinson Lagrange multiplier tests. Our results contrast with the tests for fractional unit roots, introduced by Dolado, Gonzalo, and Mayoral, which are inefficient. In the presence of short range serial correlation, we propose a simple and efficient two-step test that avoids the estimation of a nonlinear regression model. In addition, the first-order asymptotic properties of the proposed tests are not affected by the preestimation of short or long memory parameters.

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## Kinetic equation of linear fractional stable motion and applications to modeling the scaling of intermittent bursts

Fonte: The American Physical Society
Publicador: The American Physical Society

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em /04/2009
Português

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#[PACS] Fluctuation phenomena, random processes, noise, and Brownian motion#[PACS] Complex systems: Systems obeying scaling laws#Física#Fusión

Lévy flights and fractional Brownian motion have become exemplars of the heavy-tailed jumps and long-ranged memory widely seen in physics. Natural time series frequently combine both effects, and linear fractional stable motion (lfsm) is a model process of this type, combining α-stable jumps with a memory kernel. In contrast complex physical spatiotemporal diffusion processes where both the above effects compete have for many years been modeled using the fully fractional kinetic equation for the continuous-time random walk (CTRW), with power laws in the probability density functions of both jump size and waiting time. We derive the analogous kinetic equation for lfsm and show that it has a diffusion coefficient with a power law in time rather than having a fractional time derivative like the CTRW. We discuss some preliminary results on the scaling of burst “sizes” and “durations” in lfsm time series, with applications to modeling existing observations in space physics and elsewhere.; Research was carried out in part at Oak Ridge
National Laboratory, managed by UT-Battelle, LLC, for U.S. DOE under Contract No. DE-AC05-00OR22725. This research was supported in part by the EPSRC-GB, STFC, and NSF under Grant No. NSF PHY05-51164.; 9 pages...

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## Fractional Lévy motion through path integrals

Fonte: Institute of Physics
Publicador: Institute of Physics

Tipo: Artigo de Revista Científica
Formato: application/pdf

Publicado em 06/02/2009
Português

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#[PACS] Stochastic processes#[PACS] Brownian motion#[PACS] Random walks and Levy flights#Física#Fusión

Fractional Lévy motion (fLm) is the natural generalization of fractional Brownian motion in the context of self-similar stochastic processes and stable probability distributions. In this paper we give an explicit derivation of the propagator of fLm by using path integral methods. The propagators of Brownian motion and fractional Brownian motion are recovered as particular cases. The fractional diffusion equation corresponding to fLm is also obtained.; Part of this research was sponsored by the Laboratory Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy under contract number DE-AC05-00OR22725.; 8 pages, no figures.-- PACS nrs.: 02.50.Ey, 05.40.Jc, 05.40.Fb.-- ArXiv pre-print available at: http://arxiv.org/abs/0805.1838

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## Fractional diffusion models of option prices in markets with jumps

Fonte: Birkbeck, University of London, School of Economics, Mathematics and Statistics
Publicador: Birkbeck, University of London, School of Economics, Mathematics and Statistics

Tipo: info:eu-repo/semantics/submittedVersion; info:eu-repo/semantics/workingPaper
Formato: application/pdf

Publicado em 11/08/2006
Português

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#Fractional-Black-Scholes#Lévy-Stable processes#FMLS#KoBoL#CGMY#Fractional calculus#Riemann-Liouville fractional derivative#Barrier options#Down-and-out#Up-and-out#Double knock-out

Most of the recent literature dealing with the modeling of financial assets
assumes that the underlying dynamics of equity prices follow a jump process or
a Lévy process. This is done to incorporate rare or extreme events not captured
by Gaussian models. Of those financial models proposed, the most interesting
include the CGMY, KoBoL and FMLS. All of these capture some of the most
important characteristics of the dynamics of stock prices. In this article we
show that for these particular Lévy processes, the prices of financial derivatives,
such as European-style options, satisfy a fractional partial differential equation
(FPDE). As an application, we use numerical techniques to price exotic options,
in particular barrier options, by solving the corresponding FPDEs derived

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## Fractional diffusion models of option prices in markets with jumps

Fonte: Elsevier
Publicador: Elsevier

Tipo: info:eu-repo/semantics/acceptedVersion; info:eu-repo/semantics/article
Formato: application/pdf

Publicado em /02/2007
Português

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#Fractional-Black–Scholes#Lévy-stable processes#FMLS#KoBoL#CGMY#Fractional calculus#Riemann–Liouville fractional derivative#Barrier options#Down-and-out#Up-and-out#Double knock-out

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity
prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by
Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of
these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for
these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional
partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular
barrier options, by solving the corresponding FPDEs derived

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## Fractional processes: from Poisson to branching one

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 12/02/2010
Português

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Fractional generalizations of the Poisson process and branching Furry process
are considered. The link between characteristics of the processes, fractional
differential equations and Levy stable densities are discussed and used for
construction of the Monte Carlo algorithm for simulation of random waiting
times in fractional processes. Numerical calculations are performed and limit
distributions of the normalized variable Z=N/ are found for both processes.; Comment: 11 pages, 6 figures

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## Some recent advances in theory and simulation of fractional diffusion processes

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Mathematics - Probability#Mathematical Physics#Nonlinear Sciences - Chaotic Dynamics#26A33, 45K05, 47G30, 60G18, 60G50, 60G51, 60J60

To offer a view into the rapidly developing theory of fractional diffusion
processes we describe in some detail three topics of present interest: (i) the
well-scaled passage to the limit from continuous time random walk under power
law assumptions to space-time fractional diffusion, (ii) the asymptotic
universality of the Mittag-Leffler waiting time law in time-fractional
processes, (iii) our method of parametric subordination for generating particle
trajectories.; Comment: 33 pages, 3 Figures, 5 eps files. Second International Workshop on
Analysis and Numerical Approximation of Singular Problems (IWANASP 2006), 6-8
September 2006, Aegean University in Karlovassi, Samos, Greece

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## Affine representations of fractional processes with applications in mathematical finance

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 14/10/2015
Português

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#Quantitative Finance - Mathematical Finance#Mathematics - Probability#60G22 (Primary), 60G15, 60J25, 91G30 (Secondary)

Fractional processes have gained popularity in financial modeling due to the
dependence structure of their increments and the roughness of their sample
paths. The non-Markovianity of these processes gives, however, rise to
conceptual and practical difficulties in computation and calibration. To
address these issues, we show that a certain class of fractional processes can
be represented as linear functionals of an infinite dimensional affine process.
We demonstrate by means of several examples that the affine structure allows
one to construct tractable financial models with fractional features.; Comment: 43 pages

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## Maxima of stochastic processes driven by fractional Brownian motion

Fonte: Applied Probability Trust
Publicador: Applied Probability Trust

Tipo: Artigo de Revista Científica

Português

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#Keywords: Asymptotic stability#Brownian movement#Convergence of numerical methods#Differential equations#Mathematical transformations#Probability distributions#State space methods#Extreme-value theory#Fractional Brownian motion#Fractional Ornstein-Uhlenbec Extreme-value theory#Fractional Brownian motion

We study stationary processes given as solutions to stochastic differential equations driven by fractional Brownian motion. This rich class includes the fractional Ornstein-Uhlenbeck process and those processes that can be obtained from it by state space

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## Asymptotics for general nonstationary fractionally integrated processes without prehistoric influence

Fonte: Hindawi Publishing Corporation
Publicador: Hindawi Publishing Corporation

Tipo: Artigo de Revista Científica

Português

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#Keywords: Fractional processes#Functional limit theorem#Sample autocovariances and sample autocorrelations

This paper derives a functional limit theorem for general nonstationary fractionally integrated processes having no influence from prehistory. Asymptotic distributions of sample autocovariances and sample autocorrelations based on these processes are also investigated. The problem arises naturally in discussing fractionally integrated processes when the processes starts at a given initial date.

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## Estimation of fractional co-integration with unknown integration orders.

Fonte: London School of Economics and Political Science Thesis
Publicador: London School of Economics and Political Science Thesis

Tipo: Thesis; NonPeerReviewed
Formato: application/pdf

Publicado em //2004
Português

Relevância na Pesquisa

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This thesis presents different methods of estimating the co-integrating parameter in a bivariate fractionally co-integrated model. The proposed estimates enjoy optimal convergence rates and standard asymptotic distributions, yielding Wald test statistics with x2 null limit distribution. In the last few years increasing interest has developed in the issue of fractional co-integration, where both the observable series and the co-integrating error can be fractional processes, nesting the familiar situation where their respective orders are 1 and 0. These values have typically been assumed known. Chapter 1 is mainly devoted to reviewing this traditional prescription and motivate the relevance of fractional co-integration. In Chapter 2, we analyse a fully parametric model where the co-integrating gap, that is the difference between the integration order of the observables and that of the co-integrating error, is larger than 0.5. There, we show that our estimates share with the Gaussian maximum likelihood estimate the same limiting distribution, irrespective of whether the orders of integration are known or unknown, subject in the latter case to their estimation with adequate rates of convergence. Chapter 3, still in a parametric framework...

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## Investigation of electrical RC circuit within the framework of fractional calculus

Fonte: Sociedad Mexicana de Física
Publicador: Sociedad Mexicana de Física

Tipo: Artigo de Revista Científica
Formato: text/html

Publicado em 01/02/2015
Português

Relevância na Pesquisa

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In this paper, charging and discharging processes of different capacitors in electrical RC circuit are considered theoretically and experimentally. The non-local behaviors in these processes, arising from the time fractality, are investigated via fractional calculus. In this context, the time fractional differential equation related to electrical RC circuit is proposed by making use of Caputo fractional derivative. The resulting solution exhibits a feature in between power law and exponential law forms, and is obtained in terms of Mittag-Leffler function which describes physical systems with memory. The order of fractional derivative characterizes the fractality of time and being considered in the interval 0 < α ≤ 1. The traditional conclusions are recovered for α = 1, where time becomes homogenous and system has Markovian nature. By using time fractional approach, the discrepancies between the experimentally measured data and the theoretical calculations have been removed.

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