Stochastic Disorder Problems

Albert N. Shiryaev is Chief Scientific Researcher and Professor of Probability Theory and Mathematical Statistics at the Steklov Mathematical Institute of the Russian Academy of Sciences and Head of the Department of Probability Theory in the Mechanics and Mathematics Faculty at Lomonosov Moscow State University. He is the author of several books, including Problems in Probability  [translated by Andrew Lyasov], Optimal Stopping Rules [translated by A.B. Aries], and Statistics of Random Processes [with Robert S. Liptser]. He was the recipient of the A.A.MarkovPrize in 1974, of the A.N.Kolmogorov Prize in 1994, and of the Golden P.L.Chebyshev Medal of the Russian Academy of Science in 2017.

“Researchers and graduate students interested in optimal stopping, decision theory, and statistical sequential analysis will find this book useful. It is a very welcome addition to the literature of these fields.” (Rick Durrett, MAA Reviews, December 14, 2019)

• Preface.- Introduction.- Probabilistic-Statistical Models in Quickest Detection Problems. Discrete and Continuous Time.- Basic Settings and Solutions of Quickest Detection Problems. Discrete Time.- Optimal Stopping Times. General Theory for the Discrete-Time Case.- Optimal Stopping Rules. General Theory for the Discrete-Time Case in the Markov Representation.- Optimal Stopping Rules. General Theory for the Continuous-Time Case.- Basic Formulations and Solutions of Quickest Detection Problems. Continuous-Time. Models with Brownian motion.- Multi-Stage Quickest Detection of Breakdown of a Stationary Regime. Model with Brownian Motion.- Disorder on Filtered Probability Spaces.- Bayesian and Variational Problems of Hypothesis Testing. Brownian Motion Models.- Applications to Financial Mathematics.- References.- Term Index.- Notation Index.