Spectral Representation and Simulation of Fractional Brownian Motion

被引：0
作者：
Rybakov, Konstantin
机构：
[1] Independent Researcher, Moscow
来源：
COMPUTATION | 2025年 / 13卷 / 01期
关键词：
approximation; fractional Brownian motion; Legendre polynomials; simulation; spectral characteristic; spectral form of mathematical description; spectral method; STOCHASTIC CALCULUS; INTEGRATION; EQUATIONS; RESPECT;
D O I：
10.3390/computation13010019
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper gives a new representation for the fractional Brownian motion that can be applied to simulate this self-similar random process in continuous time. Such a representation is based on the spectral form of mathematical description and the spectral method. The Legendre polynomials are used as the orthonormal basis. The paper contains all the necessary algorithms and their theoretical foundation, as well as the results of numerical experiments.
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页数：28
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