Sequential Stochastic Optimization

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