Cairoli R. Sequential Stochastic Optimization 1996

Textbook in PDF format

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