On the Distribution of Multidimensional Reflected Brownian Motion

1981 ◽  
Vol 41 (2) ◽  
pp. 345-361 ◽  
Author(s):  
J. Michael Harrison ◽  
Martin I. Reiman
Keyword(s):  
Brownian Motion ◽  
Reflected Brownian Motion

Moderate deviation principle for multivalued stochastic differential equations

2019 ◽  
Vol 20 (03) ◽  
pp. 2050015 ◽  
Author(s):  
Hua Zhang
Keyword(s):  
Brownian Motion ◽  
Weak Convergence ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Moderate Deviation ◽  
Reflected Brownian Motion ◽  
Moderate Deviation Principle ◽  
Deviation Principle ◽  
Weak Convergence Approach

In this paper, we prove a moderate deviation principle for the multivalued stochastic differential equations whose proof are based on recently well-developed weak convergence approach. As an application, we obtain the moderate deviation principle for reflected Brownian motion.

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.

scholarly journals The Class of Distributions Associated with the Generalized Pollaczek-Khinchine Formula

2012 ◽  
Vol 49 (3) ◽  
pp. 883-887 ◽  
Author(s):  
Offer Kella
Keyword(s):  
Brownian Motion ◽  
Stationary Distribution ◽  
Lévy Process ◽  
Random Variables ◽  
Levy Process ◽  
Independent Random Variables ◽  
Reflected Brownian Motion ◽  
Distribution Of The Maximum ◽  
Workload Distribution ◽  
Stationary Workload

The goal is to identify the class of distributions to which the distribution of the maximum of a Lévy process with no negative jumps and negative mean (equivalently, the stationary distribution of the reflected process) belongs. An explicit new distributional identity is obtained for the case where the Lévy process is an independent sum of a Brownian motion and a general subordinator (nondecreasing Lévy process) in terms of a geometrically distributed sum of independent random variables. This generalizes both the distributional form of the standard Pollaczek-Khinchine formula for the stationary workload distribution in the M/G/1 queue and the exponential stationary distribution of a reflected Brownian motion.

scholarly journals Obliquely reflected Brownian motion in nonsmooth planar domains

2017 ◽  
Vol 45 (5) ◽  
pp. 2971-3037 ◽  
Author(s):  
Krzysztof Burdzy ◽  
Zhen-Qing Chen ◽  
Donald Marshall ◽  
Kavita Ramanan
Keyword(s):  
Brownian Motion ◽  
Reflected Brownian Motion ◽  
Planar Domains

scholarly journals A Skorohod-Type Lemma and a Decomposition of Reflected Brownian Motion

1995 ◽  
Vol 23 (2) ◽  
pp. 586-604 ◽  
Author(s):  
Krzysztof Burdzy ◽  
Ellen Toby
Keyword(s):  
Brownian Motion ◽  
Reflected Brownian Motion

scholarly journals Discrete approximations to reflected Brownian motion

2008 ◽  
Vol 36 (2) ◽  
pp. 698-727 ◽  
Author(s):  
Krzysztof Burdzy ◽  
Zhen-Qing Chen
Keyword(s):  
Brownian Motion ◽  
Reflected Brownian Motion ◽  
Discrete Approximations
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