Understanding Markov Chains
Examples and Applications
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Beschreibung
This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
This book provides an undergraduate-level introduction to discrete and continuous-time Markov chains and their applications, with a particular focus on the first step analysis technique and its applications to average hitting times and ruin probabilities. It also discusses classical topics such as recurrence and transience, stationary and limiting distributions, as well as branching processes. It first examines in detail two important examples (gambling processes and random walks) before presenting the general theory itself in the subsequent chapters. It also provides an introduction to discrete-time martingales and their relation to ruin probabilities and mean exit times, together with a chapter on spatial Poisson processes. The concepts presented are illustrated by examples, 138 exercises and 9 problems with their solutions.
Easily accessible to both mathematics and non-mathematics majors who are taking an introductory course on Stochastic Processes Filled with numerous exercises to test students' understanding of key concepts A gentle introduction to help students ease into later chapters, also suitable for self-study Accompanied with computer simulation codes in R and Python Request lecturer material: sn.pub/lecturer-material
Autor*in
Nicolas Privault
Themen in »Understanding Markov Chains«
Applications of Stochastic Processes Discrete and continuous-time Markov Chains First-step analysis in Markov Chains Gambling Processes and random walks in Markov Chains Highly accessible textbook on Stochastic Processes Introduction to Stochastic Processes Markov Chains self-study Markov Chains textbook Markov Chains textbook with examples Modern textbook on Stochastic Processes Nicolas Privault Stochastic Processes Solved problems in Markov Chains