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Adam Bobrowski - Generators of Markov Chains, Inbunden

Inbunden, Engelska, 2020

Del 190 i serien Cambridge Studies in Advanced Mathematics

Generators of Markov Chains

From a Walk in the Interior to a Dance on the Boundary

Av Adam Bobrowski

1189 kr

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Beskrivning
Elementary treatments of Markov chains, especially those devoted to discrete-time and finite state-space theory, leave the impression that everything is smooth and easy to understand. This exposition of the works of Kolmogorov, Feller, Chung, Kato, and other mathematical luminaries, which focuses on time-continuous chains but is not so far from being elementary itself, reminds us again that the impression is false: an infinite, but denumerable, state-space is where the fun begins. If you have not heard of Blackwell's example (in which all states are instantaneous), do not understand what the minimal process is, or do not know what happens after explosion, dive right in. But beware lest you are enchanted: 'There are more spells than your commonplace magicians ever dreamed of.'
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Adam Bobrowski is a professor and Chairman of the Department of Mathematics at Lublin University of Technology, Poland. He is a pure mathematician who uses the language of operator semigroups to describe stochastic processes. He has authored and co-authored nearly 70 papers on the subject, and five books, including Functional Analysis for Probability and Stochastic Processes (2005) and Convergence of One-Parameter Operator Semigroups (2016).

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'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

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