TY  - GEN
AU  - Bobrowski, Adam
TI  - Generators of Markov chains: from a walk in the interior to a dance on the boundary
SN  - 9781108495790
U1  - 519.233 
PY  - 2020///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Markov processes
KW  - Boundary theory
KW  - Dual perspective
KW  - Kato's Theorem
KW  - Generator vs Intensity matrix
N1  - Includes bibliographical references and indexes
N2  - 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.'
ER  -