WebJun 1, 2008 · The expected hitting times of Markov chains As above, let P = (p ij ) i,j∈V denote the probability transition matrix of an irreducible ape- riodic Markov chain, and pi = (pi 1 ,pi 2 ,...,pi N ) be the stationary distribution. Then 1 is the maximum eigenvalue of P with multiplicity 1, so the minimum polynomial of P is of the form q (x)= (x ... WebCalculation of hitting probabilities and mean hitting times; survival proba-bility for birth and death chains. Recall, from now on Pi stands for the probability distribution generated by …
Tree formulas, mean first passage times and Kemeny
WebMarkov chain if ˇP = ˇ, i.e. ˇis a left eigenvector with eigenvalue 1. College carbs example: 4 13; 4 13; 5 13 ˇ 0 @ 0 1=2 1=2 1=4 0 3=4 3=5 2=5 0 1 A P = 4 13; 4 13; 5 13 ˇ Rice Pasta Potato 1/2 1/2 1/4 3/4 2/5 3/5 A Markov chain reaches Equilibrium if ~p(t) = ˇfor some t. If equilibrium is reached it Persists: If ~p(t) = ˇthen ~p(t + k ... WebHere, we develop those ideas for general Markov chains. Definition 8.1 Let (Xn) ( X n) be a Markov chain on state space S S. Let H A H A be a random variable representing the hitting time to hit the set A ⊂ S A ⊂ S, given by H A = min{n ∈ {0,1,2,…}: Xn ∈ A}. H A = min { n ∈ { … reaction to popcorn in bed
Hitting times for random walks on vertex-transitive graphs
WebHitting time is the maximum expected time for the Markov chain to travel between any two states. De nition 1.4.3. Let X t be a Markov Chain on S, let V y: mintt¥0 : X t yu, and let E x denotes expectation with respect to Pp X 0 xq. The hitting time corresponding the the chain X t is t hit: max x;yPS E xpV yq: (1.8) http://www.statslab.cam.ac.uk/~yms/M3.pdf WebWe present in this note a useful extension of the criteria given in a recent paper [ Advances in Appl. Probability 8 (1976), 737–771] for the finiteness of hitting times and mean hitting … reaction to platelet infusion