Question

My Professor of Stochastic Processes gave us this challenge to be able to exempt the subject, but I cant solve it.

Stochastic Processes TOPICS: Asymptotic Properties of Markov Chains May 25, 2019 1.Consider a succession of Bernoulli experiments with probability of success (0,1),we say that a streak of length k occurs in the game n, if k successes have occurred exactly at the instant n, after a failure in the instant n-k We can model this event in a stochastic process {Xn^n in the following way; If the trial results in failure, the state is 0, if it results in success, the state is the number of successes that have occurred in succession. a)Build the transition matrix of the previous Markov Chain and explain why is it a Markov Chain? b)Show that the previous Markok Chain is irreducible, positive recurrent and aperiodic c)Find the asymptotic distribution of Markov Chain d) ¿Is the Markov Chain reversible? e Calculate the limit of the next succession when noo

Answer 1

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