A Markov process is a stochastic process for which the Markov property holds: If you know the current state, then the next state is independent of all past states.


A Markov process is any stochastic process $Y_{t}$ such that the future is conditionally independent of the past, given the present; the distribution of the process only depends on where the process is, not where it has been: $$ P(Y_{t+1}=y_{t+1} |Y_t = y_{t}, Y_{t-1} = y_{t-1}, ..., Y_{1} = y_{1}) = P(Y_{t+1}=y_{t+1} |Y_t = y_{t}) $$ This property is known as the Markov property.


The following threads on math.se provide references to resources on Markov processes: