Editing Markov property (section)

==Introduction==

A stochastic process has the Markov property if the [[conditional probability distribution]] of future states of the process (conditional on both past and present values) depends only upon the present state; that is, given the present, the future does not depend on the past. A process with this property is said to be '''Markov''' or '''Markovian''' and known as a '''[[Markov process]]'''. Two famous classes of Markov process are the [[Markov chain]] and [[Brownian motion]].

Note that there is a subtle, often overlooked and very important point that is often missed in the plain English statement of the definition: the statespace of the process is constant through time. The conditional description involves a fixed "bandwidth". For example, without this restriction we could augment any process to one which includes the complete history from a given initial condition and it would be made to be Markovian. But the state space would be of increasing dimensionality over time and does not meet the definition.