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Random Walks,In this chapter we consider our second important example of discrete-time stochastic process, which is a random walk allowed to evolve over the set . of signed integers without any boundary restriction. Of particular importance are the probabilities of return to a given state in finite time, as well as the corresponding mean return time.
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Discrete-Time Markov Chains,In this chapter we start the general study of discrete-time Markov chains by focusing on the Markov property and on the role played by transition probability matrices. We also include a complete study of the time evolution of the two-state chain, which represents the simplest example of Markov chain.
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Long-Run Behavior of Markov Chains,This chapter is concerned with the large time behavior of Markov chains, including the computation of their limiting and stationary distributions. Here the notions of recurrence, transience, and classification of states introduced in the previous chapter play a major role.
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Reliability Theory,This chapter consists in a short review of survival probabilities based on failure rate and reliability functions, in connection with Poisson processes having a time-dependent intensity.
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978-981-13-0658-7Springer Nature Singapore Pte Ltd. 2018
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Gambling Problems,te state space .. This allows us in particular to have a first look at the technique of first step analysis that will be repeatedly used in the general framework of Markov chains, particularly in Chap. ..
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