マルコフ連鎖生成器 Generators of Markov Chains : From a Walk in the Interior to a Dance on the Boundary (Cambridge Studies in Advanced Mathematics)

Bobrowski, Adam

Cambridge University Press（2020/11発売）

• 製本 Hardcover:ハードカバー版／ページ数 278 p.
• 言語 ENG
• 商品コード 9781108495790
• DDC分類 519.233

Full Description

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.'

Contents

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.