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