Eugene Dynkin is a rare example of a contemporary mathematician who has achieved results in two quite different areas of research: algebra and probability. In both areas, his ideas constitute an essential part of modern mathematical knowledge and form a basis for further development. Although his last work in algebra was published in 1955, his contributions continue to influence current research in algebra and in the physics of elementary particles. His work in probability is part of both the historical and the modern development of the topic.

Dynkin's lecture on the application of probability theory to the theory of nonlinear partial differential equations shows that all positive solutions for a class on nonlinear elliptical equations in a domain are described in terms of their traces on the boundary of the domain. While here Dynkin's main problematic tool is the theory of superdiffusio

For about half a century, two classes of stochastic processes - Gaussian processes and processes with independent increments - have played an important role in the development of stochastic analysis and its applications. During the last decade of the 20th century, a third class - branching measure-valued (BMV) processes - was also the subject of much research.

This book is devoted to the systematic exposition of the contemporary theory of controlled Markov processes with discrete time parameter or in another termi- nology multistage Markovian decision processes. We discuss the applications of this theory to various concrete problems. Particular attention is paid to mathe- matical models of economic planning, taking account of stochastic factors. The authors strove to construct the exposition in such a way that a reader interested in the applications can get through the book with a minimal mathe- matical apparatus. On the other hand, a mathematician...