Stochastic Equations and Inclusions with Mean Derivatives and Their Applications to Mathematical Physics

Abstract

This is a short introduction into the Theory of Mean Derivatives and a survey of results of the Voronezh team on the equations and inclusions with mean derivatives and their applications. In particular we explain some methods for calculation of mean derivatives, introduce the equations and inclusions with forward mean derivatives and with symmetric mean derivatives (current velocities), find optimal solutions for general inclusions and for the so called inclusions of geometric Brownian motion type, investigate the Leontieff type equations with noise and some second order equations with mean derivatives arising in mathematical physics.