scholarly journals The renormalization of self intersection local times of fractional Brownian motion

2007 ◽  
Vol 2 ◽  
pp. 2161-2178
Author(s):  
A. Rezgui
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Times ◽  
Intersection Local Times

scholarly journals α-time fractional Brownian motion: PDE connections and local times

2012 ◽  
Vol 16 ◽  
pp. 1-24 ◽  
Author(s):  
Erkan Nane ◽  
Dongsheng Wu ◽  
Yimin Xiao
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Local Times

Self-intersection local times for multifractional Brownian motion in higher dimensions: A white noise approach

2020 ◽  
Vol 23 (01) ◽  
pp. 2050007
Author(s):  
Wolfgang Bock ◽  
Jose Luis da Silva ◽  
Herry Pribawanto Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Noise Analysis ◽  
Higher Dimensions ◽  
Kernel Functions ◽  
The Self ◽  
Local Times ◽  
Multifractional Brownian Motion ◽  
White Noises ◽  
Intersection Local Times

In this paper, we study the self-intersection local times of multifractional Brownian motion (mBm) in higher dimensions in the framework of white noise analysis. We show that when a suitable number of kernel functions of self-intersection local times of mBm are truncated then we obtain a Hida distribution. In addition, we present the expansion of the self-intersection local times in terms of Wick powers of white noises. Moreover, we obtain the convergence of the regularized truncated self-intersection local times in the sense of Hida distributions.

scholarly journals Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

2019 ◽  
Vol 15 (2) ◽  
pp. 81 ◽  
Author(s):  
Herry Pribawanto Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Short Range ◽  
Probability Space ◽  
Noise Analysis ◽  
Local Times ◽  
White Noise Analysis ◽  
Self Similarity ◽  
Sample Paths

The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

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