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Intersection local times of independent fractional Brownian motions as generalized white noise functionals

Oliveira, Maria João; Silva, José Luís da; Streit, Ludwig
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Publicado em //2011 Português
Relevância na Pesquisa
76.2%
In this work we present expansions of intersection local times of fractional Brownian motions in R^d , for any dimension d ≥ 1, with arbitrary Hurst coefficients in (0, 1)^d . The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals. As an application of our approach, a sufficient condition on d for the existence of intersection local times in L^2 is derived, extending the results in Nualart and Ortiz-Latorre (J. Theoret. Probab. 20(4):759–767, 2007) to different and more general Hurst coefficients.

Self-avoiding fractional Brownian motion: the Edwards model

Grothaus, Martin; Oliveira, Maria João; Silva, José Luís da; Streit, Ludwig
Fonte: Springer Publicador: Springer
Tipo: Artigo de Revista Científica
Publicado em //2011 Português
Relevância na Pesquisa
86.29%
In this work we extend Varadhan’s construction of the Edwards polymer model to the case of fractional Brownian motions in Rd , for any dimension d ≥ 2, with arbitrary Hurst parameters H ≤ 1/d.

Intersection local times of fractional Brownian motions with H∈(0,1) as generalized white noise functionals

Drumond, Custódia; Oliveira, Maria João; Silva, José Luís da
Fonte: American Institute of Physics Publicador: American Institute of Physics
Tipo: Artigo de Revista Científica
Publicado em //2008 Português
Relevância na Pesquisa
76.24%
In R^d, for any dimension d ≥ 1, expansions of self-intersection local times of fractional Brownian motions with arbitrary Hurst coefficients in (0,1) are presented. The expansions are in terms of Wick powers of white noises (corresponding to multiple Wiener integrals), being well-defined in the sense of generalized white noise functionals.

Fractional Brownian polymers : some first results

Bornales, Jinky; Eleutério, Samuel; Oliveira, Maria João; Streit, Ludwing
Fonte: World Scientific Publicador: World Scientific
Tipo: Artigo de Revista Científica
Publicado em //2012 Português
Relevância na Pesquisa
86.29%
Recently the Edwards model for chain polymers in good solvents has been extended to include fractional Brownian motion trajectories as a description of polymer conformations. This raises in particular the question of the corresponding Flory formula for the end-to-end length of those molecules. A generalized Flory formula has been proposed, and there are some first results of numerical validations.

Self-repelling fractional Brownian motion : a generalized Edwards model for chain polymers

Bornales, Jinky; Oliveira, Maria João; Streit, Ludwing
Fonte: World Scientific Publishing Company Publicador: World Scientific Publishing Company
Tipo: Parte de Livro
Publicado em //2013 Português
Relevância na Pesquisa
96.33%
We present an extension of the Edwards model for conformations of individual chain molecules in solvents in terms of fractional Brownian motion, and discuss the excluded volume effect on the end-to-end length of such trajectories or molecules.

On the relation between the fractional Brownian motion and the fractional derivatives

Ortigueira, M.D.; Batista, A. G.
Fonte: Elsevier B.V. Publicador: Elsevier B.V.
Tipo: Artigo de Revista Científica
Publicado em /08/2008 Português
Relevância na Pesquisa
96.52%
Physics Letters A, vol. 372; Issue 7; The definition and simulation of fractional Brownian motion are considered from the point of view of a set of coherent fractional derivative definitions. To do it, two sets of fractional derivatives are considered: (a) the forward and backward and (b) the central derivatives, together with two representations: generalised difference and integral. It is shown that for these derivatives the corresponding autocorrelation functions have the same representations. The obtained results are used to define a fractional noise and, from it, the fractional Brownian motion. This is studied. The simulation problem is also considered.

A fractional linear system view of the fractional brownian motion

Ortigueira, M.D.; Batista, A. G.
Fonte: Springer Netherlands Publicador: Springer Netherlands
Tipo: Artigo de Revista Científica
Publicado em /12/2004 Português
Relevância na Pesquisa
96.41%
Nonlinear Dynamics, Vol. 38; A definition of the fractional Brownian motion based on the fractional differintegrator characteristics is proposed and studied. It is shown that the model enjoys the usually required properties. A discrete-time version based in the backward difference and in the bilinear transformation is considered. Some results are presented.

On the Clark-Ocone theorem for fractional Brownian motions with Hurst parameter bigger than half

Bender, C.; Elliott, R.
Fonte: Taylor & Francis Ltd Publicador: Taylor & Francis Ltd
Tipo: Artigo de Revista Científica
Publicado em //2003 Português
Relevância na Pesquisa
86.39%
Integration with respect to a fractional Brownian motion with Hurst parameter 1/2< H <1 is related to the inner product: In this paper we provide an example, which shows that multiplication with an indicator function can increase the corresponding norm. We discuss the significance of this result for the quasi-conditional expectation and the fractional Clark-Ocone derivative introduced in Hu and Øksendal ["Fractional White Noise Calculus and Applications to Finance", IDAQPRT , 6 (2003) 1-32]. Finally, we prove a new version of the fractional Clark-Ocone formula.; Christian Bender and Robert J. Elliott

Arbitrage in a discrete version of the Wick-Fractional Black Scholes model

Bender, C.; Elliott, R.
Fonte: Inst Operations Research Management Sciences Publicador: Inst Operations Research Management Sciences
Tipo: Artigo de Revista Científica
Publicado em //2004 Português
Relevância na Pesquisa
76.26%
We consider binary market models based on the discrete Wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage. This arbitrage is explicitly constructed in the class of self-financing one-step buy-and-hold strategies, (i.e., the investor holds shares of the stock only at one time step). Using coefficients obtained from an approximation of a fractional Brownian motion with Hurst parameter ½ < H < 1 the result is applied to a discrete version of the (Wick-)fractional Black-Scholes market.; Christian Bender and Robert J. Elliott

Fractional Black-Scholes models: complete MLE with application to fractional option pricing

Misiran, M.; Lu, Z.; Teo, K.
Fonte: Curtin UT; CD Publicador: Curtin UT; CD
Tipo: Conference paper
Publicado em //2010 Português
Relevância na Pesquisa
76.39%
Geometric fractional Brownian motion (GFBM) is an extended model of the traditional geometric Brownian motion that is widely used for Black-Scholes option pricing. By considering GFBM, we are now able to capture the memory dependency. This method will enable us to derive the estimators of the drift, _, volatility, _2, and also the index of self similarity, H, simultaneously. This will enable us to use the fractional Black-Scholes model with all the needed parameters. Simulation outcomes illustrate that our methodology is efficient and reliable. Empirical application to stock exchange index with option pricing under GFBM is also made.; Masnita Misiran, Zudi Lu and Kok Lay Teo

Risk preference based option pricing in a fractional Brownian market

Rostek, Stefan; Schöbel, Rainer
Fonte: Universität Tübingen Publicador: Universität Tübingen
Tipo: ResearchPaper
Português
Relevância na Pesquisa
86.49%
We focus on a preference based approach when pricing options in a market driven by fractional Brownian motion. Within this framework we derive formulae for fractional European options using the traditional idea of conditional expectation. The obtained formulae – as well as further results – accord with classical Brownian theory and confirm economic intuition towards fractional Brownian motion. Furthermore the influence of the Hurst parameter H on the price of a European option will be analyzed.

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

Watkins, N. W.; Credgington, D.; Sánchez, Raúl; Rosenberg, S. J.; Chapman, S. C.
Fonte: The American Physical Society Publicador: The American Physical Society
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em /04/2009 Português
Relevância na Pesquisa
76.36%
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...

Fractional Lévy motion through path integrals

Calvo, Iván; Sánchez, Raúl; Carreras, Benjamín A.
Fonte: Institute of Physics Publicador: Institute of Physics
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em 06/02/2009 Português
Relevância na Pesquisa
76.49%
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

The path integral formulation of fractional Brownian motion for the general Hurst exponent

Calvo, Iván; Sánchez, Raúl
Fonte: Institute of Physics Publicador: Institute of Physics
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em 18/07/2008 Português
Relevância na Pesquisa
86.33%
In 1995, Sebastian (1995 J. Phys. A: Math. Gen. 28 4305) gave a path integral computation of the propagator of subdiffusive fractional Brownian motion (fBm), i.e. fBm with a Hurst or self-similarity exponent H ∈ (0, 1/2). The extension of Sebastian's calculation to superdiffusion, H ∈ (1/2, 1], becomes however quite involved due to the appearance of additional boundary conditions on fractional derivatives of the path. In this communication, we address the construction of the path integral representation in a different fashion, which allows us to treat both subdiffusion and superdiffusion on an equal footing. The derivation of the propagator of fBm for the general Hurst exponent is then performed in a neat and unified way.; 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.; 5 pages, no figures.-- PACS nrs.: 05.40.-a, 02.50.Ey, 05.10.Gg.-- ArXiv preprint available at: http://arxiv.org/abs/0805.1170

A general fractional white noise theory and applications to finance

Elliott, R.; Van Der Hoek, J.
Fonte: Blackwell Publishers Publicador: Blackwell Publishers
Tipo: Artigo de Revista Científica
Publicado em //2003 Português
Relevância na Pesquisa
76.39%
We present a new framework for fractional Brownian motion in which processes with all indices can be considered under the same probability measure. Our results extend recent contributions by Hu, Øksendal, Duncan, Pasik-Duncan, and others. As an application we develop option pricing in a fractional Black-Scholes market with a noise process driven by a sum of fractional Brownian motions with various Hurst indices.; Robert J. Elliott, John Van Der Hoek; The definitive version is available at www.blackwell-synergy.com

Fractional Integral Equations and State Space Transforms

Buchmann, Boris; Klueppelberg, Claudia C
Fonte: Chapman & Hall Publicador: Chapman & Hall
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
76.31%
We introduce a class of stochastic differential equations driven by fractional Brownian motion which allow for a constructive method in order to obtain stationary solutions. This leads to a substantial extension of the fractional Ornstein-Uhlenbeck proces

Fractional Brownian Motion in Finance

Neves, Susana de Matos
Fonte: Instituto Superior de Economia e Gestão Publicador: Instituto Superior de Economia e Gestão
Tipo: Dissertação de Mestrado
Publicado em //2012 Português
Relevância na Pesquisa
96.51%
Mestrado em Matemática Financeira; Algumas das propriedades estatísticas dos dados financeiros são comuns a uma ampla variedade de mercados: a propriedade de memória longa, as caudas pesadas, assimetria (ganho / perda de assimetria), saltos, agrupamento de volatilidade, etc. A necessidade de procurar novos modelos de produtos financeiros tem aumentado nas últimas décadas devido à incapacidade dos actuais modelos explicarem algumas dessas propriedades estatísticas. Este trabalho tem como objetivo dar uma visão geral de alguns estudos que foram feitos relativamente à aplicação às finanças do movimento Browniano fracionário, em particular o trabalho de Paolo Guasoni e Cheridito Patrick, que mostram que, se assumirmos certas restrições, podemos eliminar oportunidades de arbitragem. Além disso, também são apresentados estudos empíricos com dados de mercado, com o objectivo de mostrar como se pode obter um estimador para o índice Hurst (o parâmetro do movimento Browniano fracionário). Para este fim, foram utilizados dois métodos, o método Rescaled Range e o método modificado do Rescaled Range. Este estudo permite-nos discutir o efeito de memória nas séries temporais de alguns índices de mercado.; Some of the statistical properties of the financial data are common to a wide variety of markets: long-range dependence properties...

Asymptotically optimal filtering in linear systems with fractional Brownian noises

Breton, Alain Le; Kleptsyna, Marina L.; Viot, Michel
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2004 Português
Relevância na Pesquisa
76.2%
In this paper, the filtering problem is revisited in the basic Gaussian homogeneous linear system driven by fractional Brownian motions. We exhibit a simple approximate filter which is asymptotically optimal in the sense that, when the observation time tends to infinity, the variance of the corresponding filtering error converges to the same limit as for the exact optimal filter.

An extension of sub-fractional Brownian motion

Sghir, Aissa
Fonte: Universidade Autônoma de Barcelona Publicador: Universidade Autônoma de Barcelona
Tipo: Artigo de Revista Científica Formato: application/pdf
Publicado em //2013 Português
Relevância na Pesquisa
96.48%
In this paper, firstly, we introduce and study a self-similar Gaussian process with parameters H ∈ (0; 1) and K ∈ (0; 1] that is an extension of the well known sub-fractional Brownian motion introduced by Bojdecki et al. [4]. Secondly, by using a decomposition in law of this process, we prove the existence and the joint continuity of its local time.

Maxima of stochastic processes driven by fractional Brownian motion

Buchmann, Boris; Klueppelberg, Claudia C
Fonte: Applied Probability Trust Publicador: Applied Probability Trust
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
96.53%
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