Sequential Stochastic Optimization. Wiley Series in Probability and Statistics

  • ID: 2175710
  • Book
  • 352 Pages
  • John Wiley and Sons Ltd
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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
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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.
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R. Cairoli
Robert C. Dalang
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