Generators of Markov Chains

'Western science is largely based on deducing global properties of systems from the local ones, and differential equations have proved to be a successful mathematical tool for it. It has been realized, however, that even in linear systems there can occur phase transitions that cannot be deduced from the underlying equations. Originally observed in Markov processes, the theory of phase transitions has been recently extended to general master equations. This monograph, building upon Feller's concept of the process boundary and linking it in a novel way with functional analytic tools, provides a refined analysis of the evolution beyond the phase transition. It offers a unique blend of probability and functional analysis addressing a topical problem of nonlocal and emerging properties of infinite-dimensional linear systems and largely extending the existing results.' Jacek Banasiak, University of Pretoria 'When I learned about the author's project of a book on Markov chains with denumerable state-space, I was a bit surprised and had serious reservations about it. It seemed to me that in such a simple setting all you can prove is well-known to students who took a first course in Markov processes. But with each page I read I was more convinced that I was thoroughly wrong. ... The exposition is clear and reader-friendly. The book requires only a few prerequisites. Moreover, it is autonomous and can be read without extensive knowledge of semigroup theory or stochastic processes. Personally, I hold in high regard self-contained textbooks I can read without consulting other sources. This impressive book belongs to this category.' Tomasz Szarek, University of Gdansk