Martingales and Markov Chains: Solved Exercises and Elements of Theory

ISBN-13: 9781138460331 / Angielski / Twarda / 2020

Paolo Baldi; Laurent Mazliak; Pierre Priouret

Opis

A thorough grounding in Markov chains and martingales is essential to dealing with the complex situations encountered in the study of discrete time stochastic processes. This book presents more than 100 exercises and problems related to martingales and Markov chains, each with a detailed solution.

Spis treści

Preface -- 1 Conditional Expectations -- Introduction -- Definition and First Properties -- Conditional Expectations and Conditional Laws -- Exercises -- Solutions -- 2 Stochastic Processes -- General Facts -- Stopping Times -- Exercises -- Solutions -- 3 Martingales -- First Definitions -- First Properties -- The Stopping Theorem -- Maximal Inequalities -- Square Integrable Martin g ales -- Convergence Theorems -- Regular Martin gales -- Exercises -- Problems -- Solutions -- 4 Markov Chains -- Transition Matrices, Markov Chains -- Construction and Existence -- Computations on the Canonical Chain -- Potential Operators -- Passage Problems -- Recurrence, Transience -- Recurrent Irreducible Chains -- Periodicity -- Exercises -- Problems -- Solutions -- References -- Index.

O autorze

Baldi, Paolo