Let Val X Be A Set Of States And Let T1 Tk Be A Set Of Kernels Each Of Which Satisfi 2564300

Let Val(X) be a set of states, and let T1 ,…,Tk be a set of kernels, each of which satisfies the detailed balance equation relative to some stationary distribution p. Let p1 ,…,pk be any distribution over the indexes 1,…,k. Prove that the mixture Markov chain T , which at each step takes a step sampled fromTi with probability pi , also satisfies the detailed balance equation relative to p.

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