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

2017 ◽  
Vol 855 ◽  
pp. 012050
Author(s):  
Herry P. Suryawan ◽  
Boby Gunarso
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Fractional Brownian Motion ◽  
Local Times ◽  
Mixed Fractional Brownian Motion ◽  
Intersection 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.

MULTIPLE INTERSECTION LOCAL TIMES IN TERMS OF WHITE NOISE

2001 ◽  
Vol 04 (04) ◽  
pp. 533-543 ◽  
Author(s):  
SANDRA MENDONÇA ◽  
LUDWIG STREIT
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Local Times ◽  
White Noise Functionals ◽  
Multiple Intersections ◽  
Intersection Local Times

We show how multiple intersections of Brownian motion can be expressed in terms of generalized white noise functionals. We also calculate the kernels of their chaos expansions and discuss their L2 properties.

scholarly journals White noise analysis and Tanaka formula for intersections of planar Brownian motion

1991 ◽  
Vol 122 ◽  
pp. 1-17 ◽  
Author(s):  
Narn-Rueih Shieh
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Stochastic Integral ◽  
Integral Formula ◽  
Noise Analysis ◽  
Local Times ◽  
White Noise Analysis ◽  
Planar Brownian Motion ◽  
Tanaka Formula ◽  
Intersection Local Times

In this paper, we shall use Hida’s [5, 7, 9] theory of generalized Brownian functionals (or named white noise analysis) to establish a stochastic integral formula concerning the multiple intersection local times of planar Brownian motion B(t).

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

2020 ◽  
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.

scholarly journals Existence and exponential stability in the pth moment for impulsive neutral stochastic integro-differential equations driven by mixed fractional Brownian motion

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xia Zhou ◽  
Dongpeng Zhou ◽  
Shouming Zhong
Keyword(s):  
Brownian Motion ◽  
Differential Equations ◽  
Exponential Stability ◽  
Fractional Brownian Motion ◽  
Mild Solutions ◽  
Semigroup Theory ◽  
Sufficient Conditions ◽  
Fractional Power ◽  
Banach Fixed Point Theorem ◽  
Mixed Fractional Brownian Motion

Abstract This paper consider the existence, uniqueness and exponential stability in the pth moment of mild solution for impulsive neutral stochastic integro-differential equations driven simultaneously by fractional Brownian motion and by standard Brownian motion. Based on semigroup theory, the sufficient conditions to ensure the existence and uniqueness of mild solutions are obtained in terms of fractional power of operators and Banach fixed point theorem. Moreover, the pth moment exponential stability conditions of the equation are obtained by means of an impulsive integral inequality. Finally, an example is presented to illustrate the effectiveness of the obtained results.

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