Transition Probability

Definition

A Transition Probability for a stochastic (random) system is the probability the system will transition between given states in a defined period of time.

Let us assume a state space $S ={0, \dots ,D}$. The the probability of moving from state m to state n in one time step is

$Pr(n|m)=T^{mn}$

• The collection of all transition probabilities forms the Transition Matrix which satisfies various properties.
• When the system is observed for an infinitesimal time period, we talk about the Transition Rate.

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