What is a Markov model (aka Markov Chain)? Classical Definition a discrete stochastic process X1, X2, X3, which has the Markov property PMXn1JX=X, X2=X2,.X,x,)=PXn+ X=X) (for all xi, all j, all n In words A random process which has the property that the future (next state) is conditionally independent of the past given the present(current state) Markov-a russian mathematician ca. 1922What is a Markov Model (aka Markov Chain)? Classical Definition A discrete stochastic process X1, X2, X3, … which has the Markov property: P(Xn+1 = j | X1=x1, X2=x2, … Xn=xn) = P(Xn+1 = j | Xn=x ) n (for all x , all j, all n) i In words: A random process which has the property that the future (next state) is conditionally independent of the past given the present (current state) Markov - a Russian mathematician, ca. 1922