Random, Stochastic, and Self-similar Equations

University Of Connecticut, Storrs CT

Investigators

Abstract

The proposed project consists of three parts. The first part deals with asymptotic formulas for Lyapunov exponents of differential and difference equations with small random perturbations, and estimates of the Lyapunov exponents of stochastic differential equations. The second part is devoted to the spectral problems for certain random and stochastic differential equations. The third part deals with existence and uniqueness of self-similar Dirichlet forms, diffusions, and random walks. The broader impacts of the project include applications to the study of the long term behavior of natural and statistical processes occurring in random media. Signal propagation in channels with random obstacles, electro-magnetic waves in plasma, Rossby waves in oceanography, models of financial markets are just a few of many examples of such processes. Also, the project contributes to the study of processes in self-similar objects (fractals), which have many applications in physics, engineering and biological sciences. The project includes various educational and REU activities.