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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 .
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 ...
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.
The prototypical Markov random field is the Ising model; indeed, the Markov random field was introduced as the general setting for the Ising model. [2] In the domain of artificial intelligence, a Markov random field is used to model various low- to mid-level tasks in image processing and computer vision. [3]
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.
An MRF exhibits the Markov property (= | =,) = (= | =,),for each choice of values ().Here each is the set of neighbors of .In other words, the probability that a random variable assumes a value depends on its immediate neighboring random variables.
the semigroup property: T t + s = T t ∘T s for all s, t ≥ 0; lim t → 0 ||T t f − f || = 0 for every f in C 0 (X). Using the semigroup property, this is equivalent to the map T t f from t in [0,∞) to C 0 (X) being right continuous for every f. Warning: This terminology is not uniform across the literature.
First assumption: is a Markov process on a Polish space with càdlàg paths. Second assumption: satisfies the strong Markov property. Third assumption: is quasi-left continuous on [,). Processes satisfying hypothesis (A) soon became known as Hunt processes.