Titlebook: Stationary Processes and Discrete Parameter Markov Processes; Rabi Bhattacharya,Edward C. Waymire Textbook 2022 Springer Nature Switzerlan

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Stopping Times and the Strong Markov Property,Given a stopping time ., the Markov property for discrete parameter Markov processes is extended to the conditional distribution of the process “after” time . given the .-field generated by the process up to time .. This is referred to as a strong Markov property.

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,Birth–Death Chains,Birth–death Markov chains comprise a special class of Markov processes on the integers which move to nearest neighbor states to the left or right, or stay put, in single transitions. Simple random walks provide examples for which the one-step transition probabilities do not depend on the states from which transitions are made.

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Linear Markov Processes,The linear Markov processes are most readily described in terms of evolutions obtained by i.i.d. iterated affine linear maps. This chapter addresses the ergodic theory for such processes.

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