scholarly journals Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift–-their mean value and their applications

2010 ◽  
Author(s):  
Rafał M. Łochowski
Keyword(s):  
Brownian Motion ◽  
Mean Value ◽  
Brownian Motion With Drift ◽  
Truncated Variation

scholarly journals On the double Laplace transform of the truncated variation of a Brownian motion with drift

2016 ◽  
Vol 19 (1) ◽  
pp. 281-292
Author(s):  
Rafał Marcin Łochowski
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Independent Interest ◽  
Brownian Motion With Drift ◽  
Double Laplace Transform ◽  
Truncated Variation

The aim of this paper is to find a formula for the double Laplace transform of the truncated variation of a Brownian motion with drift. In order to find the double Laplace transform, we also prove some identities for the Brownian motion with drift, which may be of independent interest.

Integral functionals under the excursion measure

2020 ◽  
Vol 57 (1) ◽  
pp. 137-155
Author(s):  
Maciej Wiśniewolski
Keyword(s):  
Brownian Motion ◽  
Local Time ◽  
Stochastic Analysis ◽  
New Method ◽  
Theoretic Approach ◽  
Integral Functionals ◽  
New Approach ◽  
Brownian Motion With Drift ◽  
Classical Potential ◽  
Excursion Measure

AbstractA new approach to the problem of finding the distribution of integral functionals under the excursion measure is presented. It is based on the technique of excursion straddling a time, stochastic analysis, and calculus on local time, and it is done for Brownian motion with drift reflecting at 0, and under some additional assumptions for some class of Itó diffusions. The new method is an alternative to the classical potential-theoretic approach and gives new specific formulas for distributions under the excursion measure.

Asymptotic variance parameters for the boundary local times of reflected Brownian motion on a compact interval

1992 ◽  
Vol 29 (04) ◽  
pp. 996-1002 ◽  
Author(s):  
R. J. Williams
Keyword(s):  
Brownian Motion ◽  
Asymptotic Variance ◽  
Hitting Time ◽  
Local Times ◽  
Compact Interval ◽  
Reflected Brownian Motion ◽  
Direct Derivation ◽  
One Dimensional ◽  
Brownian Motion With Drift ◽  
Variance Parameters

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of reflected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using an M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.

The ruin problem and cover times of asymmetric random walks and Brownian motions

2000 ◽  
Vol 32 (01) ◽  
pp. 177-192 ◽  
Author(s):  
K. S. Chong ◽  
Richard Cowan ◽  
Lars Holst
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Random Walks ◽  
Cover Time ◽  
Brownian Motions ◽  
Brownian Motion With Drift ◽  
And Brownian Motion ◽  
Cover Times ◽  
Ruin Problem

A simple asymmetric random walk on the integers is stopped when its range is of a given length. When and where is it stopped? Analogous questions can be stated for a Brownian motion. Such problems are studied using results for the classical ruin problem, yielding results for the cover time and the range, both for asymmetric random walks and Brownian motion with drift.

Sign in / Sign up

Export Citation Format

Share Document