Generators of Markov Chains
From a Walk in the Interior to a Dance on the Boundary
Seiten
2020
Cambridge University Press (Verlag)
978-1-108-49579-0 (ISBN)
Cambridge University Press (Verlag)
978-1-108-49579-0 (ISBN)
Suitable for beginning graduate students, this book discusses the theory of Markov chains, drawing on the works of Kolmogorov and Feller, and bringing the tools of functional analysis into play in a way that is not done elsewhere. The author uses numerous examples and illustrations to demonstrate the theory.
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.'
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.'
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).
A non-technical introduction; 1. A guided tour through the land of operator semigroups; 2. Generators versus intensity matrices; 3. Boundary theory: core results; 4. Boundary theory continued; 5. The dual perspective; Solutions and hints to selected exercises; Commonly used notations; References; Index.
| Erscheinungsdatum | 16.01.2021 |
|---|---|
| Reihe/Serie | Cambridge Studies in Advanced Mathematics |
| Zusatzinfo | Worked examples or Exercises; 3 Halftones, color; 4 Halftones, black and white; 6 Line drawings, black and white |
| Verlagsort | Cambridge |
| Sprache | englisch |
| Maße | 157 x 235 mm |
| Gewicht | 540 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik | |
| ISBN-10 | 1-108-49579-6 / 1108495796 |
| ISBN-13 | 978-1-108-49579-0 / 9781108495790 |
| Zustand | Neuware |
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