Markov Chains

Collection of Stochastic Processes whose effect of the past on the future is summarized only by the current state. These ones are more manageable than those depending on entire path evolution like Asian

Formally: A discrete time stochastic process $X_1,X_2,\dots$ is a markov chain if:

$P(X_{t+1}=s|X_0,X_1,\dots ,X_t)=P(X_{t+1}=s|X_t)$