Markov Processes

The book presents new methods of asymptotic analysis for nonlinearly perturbed semi-Markov processes with a finite phase space. These methods are based on special time-space screening procedures for sequential phase space reduction of semi-Markov processes combined with the systematical use of operational calculus for Laurent asymptotic expansions.

This book presents Markov and quantum processes as two sides of a coin called generated stochastic processes. It deals with quantum processes as reversible stochastic processes generated by one-step unitary operators, while Markov processes are irreversible stochastic processes generated by one-step stochastic operators. The characteristic feature of quantum processes are oscillations, interference, lots of stationary states in bounded systems and possible asymptotic stationary scattering states in open systems, while the characteristic feature of Markov processes are relaxations to a single stationary state.