Sequential Stochastic Optimization

R. Cairoli (Author), Robert C. Dalang (Author)

9780471577546, Wiley

Hardback, published 13 February 1996

352 pages
24.3 x 16.3 x 2.3 cm, 0.68 kg

Sequential Stochastic Optimization provides mathematicians andapplied researchers with a well-developed framework in whichstochastic optimization problems can be formulated and solved.Offering 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

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.

Subject Areas: Mathematics [PB]