Results 61 to 70 of about 243,967 (218)
Approximation of Fractional Brownian Motion by Martingales [PDF]
Methodology and Computing in Applied Probability, 2012 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.
Georgiy Shevchenko +4 more
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Demonstratio Mathematica, 2023 In this article, the stochastic fractional Davey-Stewartson equations (SFDSEs) that result from multiplicative Brownian motion in the Stratonovich sense are discussed.
Mohammed Wael W. +2 more
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An extension of sub-fractional Brownian motion [PDF]
Publicacions Matemàtiques, 2013 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.
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Tempered Fractional Brownian Motion with Variable Index and Variable Tempering Parameter [PDF]
arXiv, 2021 Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion with variable tempering parameter are considered.
arxiv
Option Pricing under the Subordinated Market Models
Discrete Dynamics in Nature and Society, 2022 This paper aims to study option pricing problem under the subordinated Brownian motion. Firstly, we prove that the subordinated Brownian motion controlled by the fractional diffusion equation has many financial properties, such as self-similarity ...
Longjin Lv, Changjuan Zheng, Luna Wang
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Local independence of fractional Brownian motion
Stochastic Processes and their Applications, 2009 Let S(t,t') be the sigma-algebra generated by the differences X(s)-X(s) with s,s' in the interval(t,t'), where (X_t) is the fractional Brownian motion process with Hurst index H between 0 and 1. We prove that for any two distinct t and t' the sigma-algebras S(t-a,t+a) and S(t'-a,t'+a) are asymptotically independent as a tends to 0.
Saksman, Eero, Norros, Ilkka
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An inverse random source problem for the time fractional diffusion equation driven by a fractional Brownian motion [PDF]
Inverse Problems, 2019 This paper is concerned with the mathematical analysis of an inverse random source problem for the time fractional diffusion equation, where the source is driven by a fractional Brownian motion. Given the random source, the direct problem is to study the
Xiaoli Feng, Peijun Li, Xu Wang
semanticscholar +1 more source
A Gladyshev theorem for trifractional Brownian motion and $n$-th order fractional Brownian motion [PDF]
arXiv, 2021 We prove limit theorems for the weighted quadratic variation of trifractional Brownian motion and $n$-th order fractional Brownian motion. Furthermore, a sufficient condition for the $L^P$-convergence of the weighted quadratic variation for Gaussian processes is obtained as a byproduct.
arxiv
Modelling intermittent anomalous diffusion with switching fractional Brownian motion
New Journal of Physics, 2023 The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time.
Michał Balcerek +4 more
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Estimation of the drift of fractional Brownian motion [PDF]
Statistics & Probability Letters, 2009 We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate, under the usual quadratic risk, the natural maximum likelihood estimator.
Es-Sebaiy, Khalifa +2 more
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