Markov Memoryless Property

A Markov Memoryless Property is a stochastic process property between process states where the conditional distribution on one state is only dependent on a small [math]\displaystyle{ n }[/math] number of prior states.

Example(s):
- Markov chain of order 1:
  - Weather forecasting: The weather forecast for tomorrow depends only on the weather today, and is independent of the weather yesterday or earlier.
- Markov chain of order 2:
  - Stock market prediction: The price of a stock tomorrow depends on the price of the stock today and yesterday, and is independent of the price of the stock on earlier days.
- ...
See: Markov Independence Assumption, Markov Process, Markov Chain.

References

(Wikipedia, 2021) ⇒ https://en.wikipedia.org/wiki/Markov_property Retrieved:2021-5-25.
- 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.
  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. 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 discrete-time stochastic process satisfying the Markov property is known as a Markov chain.

http://en.wikipedia.org/wiki/Markov_property
- In mathematics, the term Markov property or Markov-type property can refer to either of two closely-related things.
  In the narrowest sense, a stochastic process has the Markov property if the conditional probability distribution of future states of the process, given the present state and a constant number of past states, depend only upon the present state and the given states in the past, but not on any other past states, i.e. it is conditionally independent of these older states. Such a process is called Markovian or a Markov process. The articles Markov chain and continuous-time Markov process explore this property in greater detail.
  In a broader sense, if a stochastic process of random variables determining a set of probabilities which can be factored in such a way that the Markov property is obtained, then that process is said to have the Markov-type property ; this is defined in detail below. Useful in applied research, members of such classes defined by their mathematics or area of application are referred to as Markov random fields, and occur in a number of situations, such as the Ising model. The Markov property is named after Andrey Markov.