scholarly journals Intersection local times of fractional Brownian motions with H∈(0,1) as generalized white noise functionals

2008 ◽  
Author(s):  
Custódia Drumond ◽  
Maria João Oliveira ◽  
José Luís da Silva ◽  
Christopher C. Bernido ◽  
M. Victoria Carpio-Bernido
Keyword(s):  
White Noise ◽  
Local Times ◽  
Brownian Motions ◽  
Fractional Brownian Motions ◽  
White Noise Functionals ◽  
Intersection Local Times

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.

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 Local times for multifractional Brownian motion in higher dimensions: A white noise approach

2016 ◽  
Vol 19 (04) ◽  
pp. 1650026 ◽  
Author(s):  
Wolfgang Bock ◽  
José Luís da Silva ◽  
Herry P. Suryawan
Keyword(s):  
Brownian Motion ◽  
White Noise ◽  
Local Time ◽  
Higher Dimensions ◽  
Local Times ◽  
Multifractional Brownian Motion ◽  
White Noise Functionals ◽  
White Noises

We present the expansion of the multifractional Brownian motion (mBm) local time in higher dimensions, in terms of Wick powers of white noises (or multiple Wiener integrals). If a suitable number of kernels is subtracted, they exist in the sense of generalized white noise functionals. Moreover, we show the convergence of the regularized truncated local times for mBm in the sense of Hida distributions.

scholarly journals Hölder properties of local times for fractional Brownian motions

Metrika ◽  
2008 ◽  
Vol 69 (2-3) ◽  
pp. 125-152 ◽  
Author(s):  
D. Baraka ◽  
T. Mountford ◽  
Y. Xiao
Keyword(s):  
Local Times ◽  
Brownian Motions ◽  
Fractional Brownian Motions

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).

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