Multi-Scale Problems in Stochastic Processes
Abstract
The main goal of the project is to solve several multi-scale asymptotic problems for stochastic differential equations. The particular objectives include: - Describing the asymptotic behavior of a population for branching processes and branching diffusions when time goes to infinity and the branching mechanism is time-dependent. Developing the understanding of the critical and near-critical behavior for such processes. For branching diffusions and related processes, describing the growth of the region occupied by the particles and the phenomenon of intermittency, i.e., appearance of clusters of particles. (Branching processes are widely used in the study of evolution of various populations such as bacteria, cancer cells, sub-atomic particles, etc., where each member of the population may die (be annihilated) or produce offspring independently of the rest. Among the most important applications, branching processes are used in physics to understand nuclear chain reactions.) - Describing the limiting behavior of Markov chains (and randomly perturbed dynamical systems that can be eventually reduced to such Markov chains) when time goes to infinity and transition rates go to zero, simultaneously. The main application of such Markov chains is in the study of metastability in complex nonequilibrium systems (exhibited in climate change, genetic mutations, molecular dynamics, etc.). - Analyzing transport by randomly perturbed deterministic flows (e.g., 2- and 3-d cellular flows). Obtaining the asymptotics of the speed of front propagation in the G-equation (modeling combustion reactions) with periodic coefficients and large underlying velocity field.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Oct 11, 2018
- Source ID
- W911NF1710419
Entities
People
- Leonid Koralov
Organizations
- Army Contracting Command
- United States Army
- University of Maryland