Stopping Times and Directed Processes

A unified treatment of the theory of 'stopping times' for probability theorists and statisticians.

G. A. Edgar (Author), Louis Sucheston (Author)

9780521135085, Cambridge University Press

Paperback, published 11 March 2010

444 pages
23.4 x 15.6 x 2.3 cm, 0.62 kg

"...will be extremely valuable to anybody doing research on directed processes. It is highly original. Most of the material has been published only in research journals so far....will be an indispensable and rich source of information previously scattered throughout many journals." U. Krengel, Mathematical Reviews

The notion of 'stopping times' is a useful one in probability theory; it can be applied to both classical problems and fresh ones. This book presents this technique in the context of the directed set, stochastic processes indexed by directed sets, and many applications in probability, analysis and ergodic theory. Martingales and related processes are considered from several points of view. The book opens with a discussion of pointwise and stochastic convergence of processes, with concise proofs arising from the method of stochastic convergence. Later, the rewording of Vitali covering conditions in terms of stopping times clarifies connections with the theory of stochastic processes. Solutions are presented here for nearly all the open problems in the Krickeberg convergence theory for martingales and submartingales indexed by directed set. Another theme of the book is the unification of martingale and ergodic theorems.

Introduction
1. Stopping times
2. Infinite measure and Orlicz spaces
3. Inequalities
4. Directed index set
5. Banach-valued random variables
6. Martingales
7. Derivation
8. Pointwise ergodic theorems
9. Multiparameter processes
References
Index.

Subject Areas: Probability & statistics [PBT]