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

[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.

[发布机构] Department of Mathematics, Sanata Dharma University, Yogyakarta, Indonesia^1

[效力级别] 教育 [学科分类] 发展心理学和教育心理学

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