This book discusses probability models in which some variables vary quickly relative to others. The book will be of interest to researchers and graduate students in applied probability, physics, biology, communication theory, and stochastic processes.
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ISBN-13
978-1-4612-0627-9 (9781461206279)
DOI
10.1007/978-1-4612-0627-9
Schweitzer Klassifikation
I Prologue and Preliminaries.- 1 Introduction and Overview.- 2 Mathematical Preliminaries.- 3 Markovian Models.- II Singularly Perturbed Markov Chains.- 4 Asymptotic Expansion: Irreducible Generators.- 5 Asymptotic Normality and Exponential Bounds.- 6 Asymptotic Expansion: Weak and Strong Interactions.- 7 Weak and Strong Interactions: Asymptotic Properties and Ramification.- III Control and Numerical Methods.- 8 Markov Decision Problems.- 9 Stochastic Control of Dynamical Systems.- 10 Numerical Methods for Control and Optimization.- A Appendix.- A.1 Properties of Generators.- A.2 Weak Convergence.- A.3 Relaxed Control.- A.4 Viscosity Solutions of HJB Equations.- A.5 Value Functions and Optimal Controls.- A.6 Miscellany.- References.
