Let Q Be A Symmetric Transition Probability Matrix That Is 53 Q For All I

/in /by

Let Q be a symmetric transition probability matrix, that is qy qu for all i,j- 1,… ,N. Consider a Markov chain which, when the present state is i, generates the value of a random variable X such that P(X j) dy, and if X-j, then either moves to state j with probability b,/(b, + bi), or remains in state i otherwise, where b,, j-1,…, N, are specified positive numbers. Show that the resulting Markov chain is time reversible with stationary probabilities a Cb,, j1,.., N

2. Let Q be a symmetric transition probability matrix, that is, 53,- }- = q},- for alli, j. Consider a Markov chain which, when the present state is i, generatesthe value of a raindom variable X such that P{X = j} = (3,}, and if X = j,then either moves to state j with probability b}- /(b,- + bf), or remains in state1′ otherwise, where b}, j = l . . . , N, are specified positive numbers. Show that the resulting Markov chain is time reversible with limiting probabilities

 
"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"
ORDER NOW