Publisher Description

Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and much material that is either new or has never beforeappeared in book form, it lucidly presents a unified theory ofoptimal stopping and optimal sequential control of stochasticprocesses. This book has been carefully organized so that littleprior knowledge of the subject is assumed; its only prerequisitesare a standard graduate course in probability theory and somefamiliarity 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 ofpartial sums of arrays of independent random variables
* The general theory of optimal stopping for processes indexed byInd
* Structural properties of information flows
* Sequential sampling and the theory of optimal sequential control
* Multi-armed bandits, Markov chains and optimal switching betweenrandom walks

Back Cover

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

Flap

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

Table of Contents

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.

Long Description

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

Feature

Includes several applications such as sequential statistical testing involving several populations and the multi-armed bandit problem. Extensive problems and real-life examples are used throughout the book. Provides a well-developed framework in which stochastic optimization problems can be formulated and solved.

Details