Reflected Brownian Motion in Time Dependent Domains

2014 ◽  
pp. 107-131
Author(s):  
Krzysztof Burdzy
Keyword(s):  
Brownian Motion ◽  
Time Dependent ◽  
Reflected Brownian Motion

scholarly journals The heat equation and reflected Brownian motion in time-dependent domains

2004 ◽  
Vol 32 (1B) ◽  
pp. 775-804 ◽  
Author(s):  
John Sylvester ◽  
Zhen-Qing Chen ◽  
Krzysztof Burdzy
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Time Dependent ◽  
Reflected Brownian Motion

scholarly journals The heat equation and reflected Brownian motion in time-dependent domains.

2003 ◽  
Vol 204 (1) ◽  
pp. 1-34 ◽  
Author(s):  
Krzysztof Burdzy ◽  
Zhen-Qing Chen ◽  
John Sylvester
Keyword(s):  
Brownian Motion ◽  
Heat Equation ◽  
Time Dependent ◽  
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.

scholarly journals Large deviations for the boundary local time of doubly reflected Brownian motion

2015 ◽  
Vol 96 ◽  
pp. 262-268 ◽  
Author(s):  
Martin Forde ◽  
Rohini Kumar ◽  
Hongzhong Zhang
Keyword(s):  
Brownian Motion ◽  
Large Deviations ◽  
Local Time ◽  
Reflected Brownian Motion

scholarly journals A generalized perspective of Fourier and Fick’s laws: Magnetized effects of Cattaneo-Christov models on transient nanofluid flow between two parallel plates with Brownian motion and thermophoresis

2020 ◽  
Vol 9 (1) ◽  
pp. 201-222 ◽  
Author(s):  
Usha Shankar ◽  
Neminath B. Naduvinamani ◽  
Hussain Basha
Keyword(s):  
Brownian Motion ◽  
Joule Heating ◽  
Concentration Field ◽  
Double Diffusion ◽  
Diffusion Models ◽  
Time Dependent ◽  
Parallel Plates ◽  
Nanofluid Flow ◽  
Casson Nanofluid ◽  
Highly Nonlinear

AbstractPresent research article reports the magnetized impacts of Cattaneo-Christov double diffusion models on heat and mass transfer behaviour of viscous incompressible, time-dependent, two-dimensional Casson nanofluid flow through the channel with Joule heating and viscous dissipation effects numerically. The classical transport models such as Fourier and Fick’s laws of heat and mass diffusions are generalized in terms of Cattaneo-Christov double diffusion models by accounting the thermal and concentration relaxation times. The present physical problem is examined in the presence of Lorentz forces to investigate the effects of magnetic field on double diffusion process along with Joule heating. The non-Newtonian Casson nanofluid flow between two parallel plates gives the system of time-dependent, highly nonlinear, coupled partial differential equations and is solved by utilizing RK-SM and bvp4c schemes. Present results show that, the temperature and concentration distributions are fewer in case of Cattaneo-Christov heat and mass flux models when compared to the Fourier’s and Fick’s laws of heat and mass diffusions. The concentration field is a diminishing function of thermophoresis parameter and it is an increasing function of Brownian motion parameter. Finally, an excellent comparison between the present solutions and previously published results show the accuracy of the results and methods used to achieve the objective of the present work.

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

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

Moments of certain stochastic integrals occurring in mathematical physics

1992 ◽  
Vol 120 (3-4) ◽  
pp. 267-282 ◽  
Author(s):  
Lieven Smits
Keyword(s):  
Brownian Motion ◽  
Vector Field ◽  
Mathematical Physics ◽  
Time Dependent ◽  
Regularity Conditions ◽  
Stochastic Integrals ◽  
Cauchy Problems ◽  
Dependent Vector ◽  
Set Up

SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.

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