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  2. Markov property - Wikipedia

    en.wikipedia.org/wiki/Markov_property

    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 .

  3. Markov decision process - Wikipedia

    en.wikipedia.org/wiki/Markov_decision_process

    The "Markov" in "Markov decision process" refers to the underlying structure of state transitions that still follow the Markov property. The process is called a "decision process" because it involves making decisions that influence these state transitions, extending the concept of a Markov chain into the realm of decision-making under uncertainty.

  4. Markov operator - Wikipedia

    en.wikipedia.org/wiki/Markov_operator

    In probability theory and ergodic theory, a Markov operator is an operator on a certain function space that conserves the mass (the so-called Markov property). If the underlying measurable space is topologically sufficiently rich enough, then the Markov operator admits a kernel representation. Markov operators can be linear or non-linear.

  5. Markov model - Wikipedia

    en.wikipedia.org/wiki/Markov_model

    In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state. An example use of a Markov chain is Markov chain Monte Carlo, which uses the Markov property to prove that a particular method for performing a random walk will sample from the joint distribution.

  6. Markov random field - Wikipedia

    en.wikipedia.org/wiki/Markov_random_field

    In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties.

  7. Partition function (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Partition_function...

    The partition function occurs in many problems of probability theory because, in situations where there is a natural symmetry, its associated probability measure, the Gibbs measure, has the Markov property.

  8. Renewal theory - Wikipedia

    en.wikipedia.org/wiki/Renewal_theory

    The renewal function satisfies a recursive integral equation, the renewal equation. ... The Poisson process is the unique renewal process with the Markov property, [1

  9. Feller process - Wikipedia

    en.wikipedia.org/wiki/Feller_process

    A Feller transition function is a probability transition function ... satisfies the strong Markov property with respect to the filtration (+), i.e., for ...