In probability theory and statistics, the term Markov property refers to the memoryless property of a stochastic process. It is named after the Russian mathematician Andrey Markov.
A stochastic process has the Markov property if the conditional probability distribution of future states of the process depends only upon the present state, not on the sequence of events that preceded it. A process with this property is called a Markov process. The term strong Markov property is similar to the Markov property, except that the meaning of "present" is defined in terms of a random variable known as a stopping time. Both the terms "Markov property" and "strong Markov property" have been used in connection with a particular "memoryless" property of the exponential distribution.
The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model.
A Markov random field, extends this property to two or more dimensions or to random variables defined for an interconnected network of items. An example of a model for such a field is the Ising model.
A system with discrete-time processes with the Markov property is known as a Markov chain.
Read more about Markov Property: Introduction, Definition, Strong Markov Property, Alternative Formulations, Applications
Famous quotes containing the word property:
“Let’s call something a rigid designator if in every possible world it designates the same object, a non-rigid or accidental designator if that is not the case. Of course we don’t require that the objects exist in all possible worlds.... When we think of a property as essential to an object we usually mean that it is true of that object in any case where it would have existed. A rigid designator of a necessary existent can be called strongly rigid.”
—Saul Kripke (b. 1940)