A Markov process is a stochastic process that has the Markov property. In other words, a stochastic process is called a Markov process if at every time *t*, the conditional probability law of the process given the past depends only on the present state. Intuitively, a Markov process is a process that does not have memory. In this chapter, we present the mathematical definition of Markov processes and relevant results.

**Definition 29.1** (Conditional Independence). Let (Ω, , *P*) be a probability space. Let be sub-σ-algebras of . Then are said to be conditionally independent given if

where *V*_{i} is an arbitrary positive random variable in *m*_{i}, *i* = 1, 2,…, *n*. Here *m*_{i} is the set of all _{i}-measurable functions.

**Definition 29.2** (Markov Process). Let ...

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