Sequential Stochastic Optimization

ISBN-13: 9780471577546 / Angielski / Twarda / 1996 / 352 str.

R. Cairoli; Robert C. Dalang

Opis

Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-parameter martingales.

Major topics covered in Sequential Stochastic Optimization include:
* Fundamental notions, such as essential supremum, stopping points, accessibility, martingales and supermartingales indexed by INd
* Conditions which ensure the integrability of certain suprema of partial sums of arrays of independent random variables
* The general theory of optimal stopping for processes indexed by Ind
* Structural properties of information flows
* Sequential sampling and the theory of optimal sequential control
* Multi-armed bandits, Markov chains and optimal switching between random walks

Spis treści

Preliminaries.

Sums of Independent Random Variables.

Optimal Stopping.

Reduction to a Single Dimension.

Accessibility and Filtration Structure.

Sequential Sampling.

Optimal Sequential Control.

Multiarmed Bandits.

The Markovian Case.

Optimal Switching Between Two Random Walks.

Bibliography.

Indexes.