​Michel Benaïm is a full professor and the head of the probability group at the University of Neuchâtel. He has taught at the universities of Toulouse, Cergy-Pontoise, Ecole Normale Supérieure de Cachan (now Paris-Saclay) and Ecole Polytechnique. Together with Nicole El Karoui, he is the author of the textbook Promenade Aléatoire. He has worked extensively on problems at the interface of probability theory and dynamical systems. He is a member of the editorial boards of Journal of Dynamics and Games, the Springer collection Mathématiques et Applications, and Stochastic Processes and their Applications.Tobias Hurth received his Ph.D. in mathematics from the Georgia Institute of Technology in 2014. He has since held postdoctoral positions at the University of Toronto, the Ecole Polytechnique Fédérale de Lausanne, and the University of Neuchâtel. His research interests include stochastic processes, random dynamics, and mathematical physics.

“The book is written in a rigorous style. … There is a large number of very useful exercises, in some cases with short hints. … the material in this book is suitable for master programs at good universities. Solving the exercises would take serious efforts, however this will guarantee a great knowledge in Markov chains, in metric spaces and their ergodicity. …” (Jordan M. Stoyanov, zbMATH 1514.60001, 2023)

• 1 Markov Chains.- 2 Countable Markov Chains.- 3 Random Dynamical Systems.- 4  Invariant and Ergodic Probability Measures.- 5 Irreducibility.- 6 Petite Sets and Doeblin points.- 7 Harris and Positive Recurrence.- 8 Harris Ergodic Theorem.

​Michel Benaïm is a full professor and the head of the probability group at the University of Neuchâtel. He has taught at the universities of Toulouse, Cergy-Pontoise, Ecole Normale Supérieure de Cachan (now Paris-Saclay) and Ecole Polytechnique. Together with Nicole El Karoui, he is the author of the textbook Promenade Aléatoire. He has worked extensively on problems at the interface of probability theory and dynamical systems. He is a member of the editorial boards of Journal of Dynamics and Games, the Springer collection Mathématiques et Applications, and Stochastic Processes and their Applications.Tobias Hurth received his Ph.D. in mathematics from the Georgia Institute of Technology in 2014. He has since held postdoctoral positions at the University of Toronto, the Ecole Polytechnique Fédérale de Lausanne, and the University of Neuchâtel. His research interests include stochastic processes, random dynamics, and mathematical physics.

“The book is written in a rigorous style. … There is a large number of very useful exercises, in some cases with short hints. … the material in this book is suitable for master programs at good universities. Solving the exercises would take serious efforts, however this will guarantee a great knowledge in Markov chains, in metric spaces and their ergodicity. …” (Jordan M. Stoyanov, zbMATH 1514.60001, 2023)

• 1 Markov Chains.- 2 Countable Markov Chains.- 3 Random Dynamical Systems.- 4  Invariant and Ergodic Probability Measures.- 5 Irreducibility.- 6 Petite Sets and Doeblin points.- 7 Harris and Positive Recurrence.- 8 Harris Ergodic Theorem.

​Michel Benaïm is a full professor and the head of the probability group at the University of Neuchâtel. He has taught at the universities of Toulouse, Cergy-Pontoise, Ecole Normale Supérieure de Cachan (now Paris-Saclay) and Ecole Polytechnique. Together with Nicole El Karoui, he is the author of the textbook Promenade Aléatoire. He has worked extensively on problems at the interface of probability theory and dynamical systems. He is a member of the editorial boards of Journal of Dynamics and Games, the Springer collection Mathématiques et Applications, and Stochastic Processes and their Applications.Tobias Hurth received his Ph.D. in mathematics from the Georgia Institute of Technology in 2014. He has since held postdoctoral positions at the University of Toronto, the Ecole Polytechnique Fédérale de Lausanne, and the University of Neuchâtel. His research interests include stochastic processes, random dynamics, and mathematical physics.

“The book is written in a rigorous style. … There is a large number of very useful exercises, in some cases with short hints. … the material in this book is suitable for master programs at good universities. Solving the exercises would take serious efforts, however this will guarantee a great knowledge in Markov chains, in metric spaces and their ergodicity. …” (Jordan M. Stoyanov, zbMATH 1514.60001, 2023)

• 1 Markov Chains.- 2 Countable Markov Chains.- 3 Random Dynamical Systems.- 4  Invariant and Ergodic Probability Measures.- 5 Irreducibility.- 6 Petite Sets and Doeblin points.- 7 Harris and Positive Recurrence.- 8 Harris Ergodic Theorem.