Transition Probability

Definition

Suppose the conditional probability of $X_{n+1}$ being in state $j$ given that $X_n$ is in state $i$ is constant over time:

$P_{ij}=P(X_{n+1}=j\mid X_n=i),\text{for all }n$

Then $P_{ij}$ is called the one-step transition probability.

Interpretation

Transition probability $P_{ij}$ is the probability of transitioning from state $i$ to state $j$ in one time step.

Related

• Transition Probability Matrix
• n-step Transition Matrix
• Chapman-Kolmogorov Equation