Markov property

When the behavior of a stochastic process {X(t), t ∈ T} at times in the future depends only on the present state of the process (past behavior of the process affects the future behavior only through the present state of the process); that is, for any n > 0, any set of time points t ₁ < t ₂ <... < t _n < t _n+1 in the time domain T, and any states x ₁, x ₂,..., x _n and any set A in the same space, Pr{X(t _n+1) ∈ A|X(t ₁) = x ₁,..., X(t _n) = x _n} = Pr{X(t _n+1) ∈ A|X(t _n) = x _n}. Markov chains; Markov processes.