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Long Time Behavior of Finite and Infinite Dimensional Reflected Brownian Motions
Sayan Banerjee, Amarjit Budhiraja
This article presents a review of some old and new results on the long time behavior of reflected diffusions. First, we present a summary of prior results on construction, ergodici…
Extremal Invariant Distributions of Infinite Brownian Particle Systems with Rank Dependent Drifts
Sayan Banerjee, Amarjit Budhiraja
\noindent Consider an infinite collection of particles on the real line moving according to independent Brownian motions and such that the -th particle from the left gets the dr…
Large Deviations for Small Noise Diffusions Over Long Time
Amarjit Budhiraja, Pavlos Zoubouloglou
We study two problems. First, we consider the large deviation behavior of empirical measures of certain diffusion processes as, simultaneously, the time horizon becomes large and n…
Empirical Measure Large Deviations for Reinforced Chains on Finite Spaces
Amarjit Budhiraja, Adam Waterbury
Let be a transition probability kernel on a finite state space such that for all . Consider a reinforced chain given as a seque…
The Inert Drift Atlas Model
Sayan Banerjee, Amarjit Budhiraja, Benjamin Estevez
Consider a massive (inert) particle impinged from above by N Brownian particles that are instantaneously reflected upon collision with the inert particle. The velocity of the inert…