This book is devoted to new trends in random evolution and their applications to the stochastic evolutionary system. It contains new developments such as an analogue of Dynkin’s formula, boundary value problems, stability and control of random evolutions, stochastic evolutionary equations, and driven martingale measures. In addition, it treats statistics of random evolutions processes, statistics of financial stochastic models, and stochastic stability and control of financial markets. Audience: This volume will be of interest to research and applied mathematicians working in the fields of applied probability, stochastic processes, and random evolutions, as well as experts in statistics, finance and insurance.