6 papers
Limiting Behavior of Randomly Perturbed Diffusions with Invariant Repelling Surfaces
Leonid Koralov, Chenglin Liu
We study small perturbations of diffusion processes in that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unp…
Distribution of particles near the front in supercritical branching Brownian motion with compactly supported branching
Pratima Hebbar, Leonid Koralov
We investigate the long-time behavior of a dimensional supercritical branching Brownian motion with a compactly supported branching potential. It is known that, for $\mathbf{v}…
Spectral properties of operators and wave propagation in high-contrast media
Yuri A. Godin, Leonid Koralov, Boris Vainberg
The paper aims to study the spectral properties of elliptic operators with highly inhomogeneous coefficients and related issues concerning wave propagation in high-contrast media.…
Energy growth for systems of coupled oscillators with partial damping
Dmitry Dolgopyat, Bassam Fayad, Leonid Koralov +1
We consider two interacting particles on the circle. The particles are subject to stochastic forcing, which is modeled by white noise. In addition, one of the particles is subject…
Local limit theorem for time-inhomogeneous functions of Markov processes
Leonid Koralov, Shuo Yan
In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in…
Metastable Distributions of Semi-Markov Processes
Leonid Koralov, Ishfaaq Mohammed Imtiyas
In this paper, we consider semi-Markov processes whose transition times and transition probabilities depend on a small parameter . Understanding the asymptotic behavio…