Generators of Markov chains: from a walk in the interior to a dance on the boundary

By:

Bobrowski, Adam

Series: Cambridge Studies in Advanced Mathematics ; 190Publication details: Cambridge University Press, 2020. Cambridge:Description: xvii, 260p. : ill. ; hb, 23 cmISBN:

9781108495790

Subject(s):

DDC classification:

519.233 BOB

Summary: 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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Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	519.233 BOB (Browse shelf(Opens below))	1	Available		030101

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Previous	519.23 BOV Gaussian processes on trees: from spin glasses to branching Brownian motion	519.23 KAR Introduction to stochastic calculus	519.23 NUA Introduction to Malliavin calculus	519.233 BOB Generators of Markov chains: from a walk in the interior to a dance on the boundary	519.233 BOV Metastability: a potential theoretic approach	519.233 FRE Markov processes and differential equations: asymptotic problems	519.233 KAL Stochastic analysis and diffusion processes	Next

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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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