oalib
Search Results: 1 - 10 of 100 matches for " "
All listed articles are free for downloading (OA Articles)
Page 1 /100
Display every page Item
A fractional Brownian motion model for the turbulent refractive index in lightwave propagation  [PDF]
Dario G. Perez,Luciano Zunino,Mario Garavaglia
Physics , 2003, DOI: 10.1016/j.optcom.2004.08.007
Abstract: It is discussed the limitations of the widely used markovian approximation applied to model the turbulent refractive index in lightwave propagation. It is well-known the index is a passive scalar field. Thus, the actual knowledge about these quantities is used to propose an alternative stochastic process to the markovian approximation: the fractional Brownian motion. This generalizes the former introducing memory; that is, there is correlation along the propagation path.
The fractional Brownian motion property of the turbulent refractive within Geometric Optics  [PDF]
Dario G. Perez
Physics , 2003,
Abstract: We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the refractive index properties, but they are not differentiable. We overcome the apparent impossibility of their use within the Ray Optics approximation introducing a Stochastic Calculus. Afterwards, we successfully provide a solution for the stochastic ray-equation; moreover, its implications in the statistical analysis of experimental data is discussed. In particular, we analyze the dependence of the averaged solution against the characteristic variables of a simple propagation problem.
Fractional Brownian Motion Limit for a Model of Turbulent Transport  [PDF]
Albert Fannjiang,Tomasz Komorowski
Mathematics , 1999,
Abstract: Passive scalar motion in a family of random Gaussian velocity fields with long-range correlations is shown to converge to persistent fractional Brownian motions in long times.
The fractional Brownian motion property of the turbulent refractive index and the Fermat's Extremal Principle  [PDF]
Dario G Perez
Physics , 2002,
Abstract: We introduce fractional Brownian motion processes (fBm) as an alternative model for the turbulent index of refraction. These processes allow to reconstruct most of the index properties, but they are not differentiable. We overcome the apparent impossibility of their use in the variational equation coming from the Fermat's Principle with the introduction of a Stochastic Calculus. Afterwards, we successfully provide a solution for the stochastic ray equation; moreover, its implications in the statistical analysis of experimental data is discussed.
The Multiparameter Fractional Brownian Motion  [PDF]
Erick Herbin,Ely Merzbach
Mathematics , 2006,
Abstract: We define and study the multiparameter fractional Brownian motion. This process is a generalization of both the classical fractional Brownian motion and the multiparameter Brownian motion, when the condition of independence is relaxed. Relations with the L\'evy fractional Brownian motion and with the fractional Brownian sheet are discussed. Different notions of stationarity of the increments for a multiparameter process are studied and applied to the fractional property. Using self-similarity we present a characterization for such processes. Finally, behavior of the multiparameter fractional Brownian motion along increasing paths is analysed.
Approximations of fractional Brownian motion  [PDF]
Yuqiang Li,Hongshuai Dai
Statistics , 2012, DOI: 10.3150/10-BEJ319
Abstract: Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the one-parameter fractional Brownian motion is constructed using a two-parameter Poisson process. The proof involves the tightness and identification of finite-dimensional distributions.
On the mixed fractional Brownian motion  [PDF]
Mounir Zili
International Journal of Stochastic Analysis , 2006, DOI: 10.1155/jamsa/2006/32435
Abstract: The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the α-differentiability of its sample paths.
Approximation of fractional Brownian motion by martingales  [PDF]
Sergiy Shklyar,Georgiy Shevchenko,Yuliya Mishura,Vadym Doroshenko,Oksana Banna
Mathematics , 2012, DOI: 10.1007/s11009-012-9313-8
Abstract: We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.
Fractional Brownian motion in a nutshell  [PDF]
Georgiy Shevchenko
Mathematics , 2014,
Abstract: This is an extended version of the lecture notes to a mini-course devoted to fractional Brownian motion and delivered to the participants of 7th Jagna International Workshop.
Results on the Supremum of Fractional Brownian Motion  [PDF]
Ceren Vardar
Mathematics , 2009,
Abstract: We show that the distribution of the square of the supremum of reflected fractional Brownian motion up to time a, with Hurst parameter-H greater than 1/2, is related to the distribution of its hitting time to level $1,$ using the self similarity property of fractional Brownian motion. It is also proven that second moment of supremum of reflected fractional Brownian motion up to time $a$ is bounded above by $a^{2H}.$ Similar relations are obtained for the supremum of fractional Brownian motion with Hurst parameter greater than 1/2, and its hitting time to level $1.$ What is more, we obtain an upper bound on the complementary probability distribution of the supremum of fractional Brownian motion and reflected fractional Brownian motion up to time a, using Jensen's and Markov's inequalities. A sharper bound is observed on the distribution of the supremum of fractional Brownian motion by the properties of Gamma distribution. Finally, applications of the given results to the financial markets are investigated and partial results are provided.
Page 1 /100
Display every page Item


Home
Copyright © 2008-2017 Open Access Library. All rights reserved.