Self-Intersection Local Times of Generalized Mixed Fractional Brownian Motion as White Noise Distributions

International Conference on Mathematics: Education, Theory and Application

数学;教育

Suryawan, Herry P.^1 ; Gunarso, Boby^1

Department of Mathematics, Sanata Dharma University, Yogyakarta, Indonesia^1

关键词: Fractional brownian motion;    Linear combinations;    Mixed fractional Brownian motion;    Noise distribution;    Self similarity properties;    Self-intersections;    Stationary increments;    White noise analysis;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/855/1/012050/pdf
DOI  :  10.1088/1742-6596/855/1/012050

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

The generalized mixed fractional Brownian motion is defined by taking linear combinations of a finite number of independent fractional Brownian motions with different Hurst parameters. It is a Gaussian process with stationary increments, posseses self-similarity property, and, in general, is neither a Markov process nor a martingale. In this paper we study the generalized mixed fractional Brownian motion within white noise analysis framework. As a main result, we prove that for any spatial dimension and for arbitrary Hurst parameter the self-intersection local times of the generalized mixed fractional Brownian motions, after a suitable renormalization, are well-defined as Hida white noise distributions. The chaos expansions of the self-intersection local times in the terms of Wick powers of white noises are also presented.