Markov Property

Definition

Let $\{X_t\}$ be a stochastic process.

The Markov Property states that, given the value of $X_t$, the values of $X_s$ for $s>t$ are not influenced by the values of $X_u$ for $u<t$.

$P\{X_{n+1}=j\mid X_n=i,X_{n-1}=i_{n-1},\dots ,X_0=i_0\}=P\{X_{n+1}=j\mid X_n=i\}$

Interpretation

The probability of any particular future behavior of the process, when its current state is known exactly, is not altered by additional knowledge concerning its past behavior.

Related

• Markov Process
• Discrete-time Markov Chain