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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. [1] An example of a model for such a field is the Ising model.
The memorylessness property asserts that the number of previously failed trials has no effect on the number of future trials needed for a success. Geometric random variables can also be defined as taking values in N 0 {\displaystyle \mathbb {N} _{0}} , which describes the number of failed trials before the first success in a sequence of ...
A Markov process is a stochastic process that satisfies the Markov property (sometimes characterized as "memorylessness"). In simpler terms, it is a process for which predictions can be made regarding future outcomes based solely on its present state and—most importantly—such predictions are just as good as the ones that could be made ...
We will assume for the moment that all state spaces of the systems considered, classical or quantum, are finite-dimensional. The memoryless in the section title carries the same meaning as in classical information theory: the output of a channel at a given time depends only upon the corresponding input and not any previous ones.
A memoryless source is one in which each message is an independent identically distributed random variable, whereas the properties of ergodicity and stationarity impose less restrictive constraints. All such sources are stochastic. These terms are well studied in their own right outside information theory.
This guess is not improved by the added knowledge that one started with $10, then went up to $11, down to $10, up to $11, and then to $12. The fact that the guess is not improved by the knowledge of earlier tosses showcases the Markov property, the memoryless property of a stochastic process. [1]
The Markov property, the memoryless property of a stochastic process The Markovians, an extinct god-like species in Jack L. Chalker's Well World series of novels Markovian Parallax Denigrate , references a mysterious series of Usenet messages
The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution. [1]: 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.