Definition:Markov Process

Definition

Let $X$ be a continuous random variable which varies over time.

Let $X_t$ denote the value of $X$ at time $t$.

Then $X$ is a Markov process if and only if the future behaviour of $X$ is dependent only upon the value of $X$ at the present time.

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Also known as

A Markov process is also known as a Markov chain.

However, the latter term is usually reserved for a stochastic process whose transition times consist of a countable sequence and whose state space is also countable.

Some sources use the spelling Markoff process.

Also see

• Results about Markov processes can be found here.

Source of Name

This entry was named for Andrey Andreyevich Markov.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Markov chain
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Markov chain