Finite Markov Chains - Part I
(2.1) P(Xt+1 = xi | X1 = xk,1 , … , Xt = xk,t) = P(Xt+1 = xi | Xt = xk,t)
(2.2) P(X1 = xk,1 , … , Xt = xk,t , Xt+1 = xi ) =
P(Xt+1 = xi | Xt = xk,t) P(Xt = xk,t | Xt-1 = xk,t-1 ) … P(X2 = xk,2| X1 = xk,1) P(X1 = xk,1)
(2.3) P(X1 = xk,1 , … , Xt = xk,t , Xt+1 = xi ) = P(xk,t , xt) P(xk,t-1, xj,t) … P(xk,1, xk,2) P(X1 = xk,1)