Markov Property dependency structure of Xo,X1,X2,... ●Markov property: (memoryless) X+1 depends only on X: ∀t=0,1,2,.,c0,c1,.,xt-1,x,y∈2 Pr[Xt+1=y Xo =Jo;...,Xt-1=xt-1,Xt= =PrX:+1=y Xi=x Markov chain:discrete time discrete space stochastic process with Markov property.Markov Property • dependency structure of • Markov property: X0, X1, X2,... (memoryless) Xt+1 depends only on Xt Pr[Xt+1 = y | X0 = x0,...,Xt￾1 = xt￾1, Xt = x] = Pr[Xt+1 = y | Xt = x] 8t = 0, 1, 2,..., 8x0, x1,...,xt￾1, x, y 2 ⌦ Markov chain: discrete time discrete space stochastic process with Markov property