Question: Consider a regular continuous time Markov chain X_t on {0,1} with rates q_{0,1}=q_{1,0}=lambda > 0. Assume that P(X_0=0)=P(X_0=1). Define {S_n, n>=1} to be the successive

Consider a regular continuous time Markov chain X_t on {0,1} with rates q_{0,1}=q_{1,0}=lambda > 0. Assume that P(X_0=0)=P(X_0=1). Define {S_n, n>=1} to be the successive return times to 0 for t>0. Calculate Cov(S_1,S_2).

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