'This monograph is suitable for graduate students and researchers who have a good background in probability theory and analysis and have mastered such key topics as martingales, stochastic calculus and weak convergence, on the one hand, and the analytic theory of semigroups, on the other hand. ... This book is pioneering in developing a new and important type of dynamics for modelling complex stochastic systems. It deserves to be widely read.' Bulletin of the London Mathematical Society '... this is an important book. Written with great care by a leading expert, it is accessible to researchers and graduate students in stochastic and functional analysis, with applications in mathematical physics and systems biology.' Mathematical Reviews