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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 model - Wikipedia

    en.wikipedia.org/wiki/Markov_model

    The simplest Markov model is the Markov chain.It models the state of a system with a random variable that changes through time. In this context, the Markov property indicates that the distribution for this variable depends only on the distribution of a previous state.

  4. Feller process - Wikipedia

    en.wikipedia.org/wiki/Feller_process

    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.

  5. Markov chain - Wikipedia

    en.wikipedia.org/wiki/Markov_chain

    Markov chains and continuous-time Markov processes are useful in chemistry when physical systems closely approximate the Markov property. For example, imagine a large number n of molecules in solution in state A, each of which can undergo a chemical reaction to state B with a certain average rate. Perhaps the molecule is an enzyme, and the ...

  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. 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.

  8. Hammersley–Clifford theorem - Wikipedia

    en.wikipedia.org/wiki/Hammersley–Clifford_theorem

    The Hammersley–Clifford theorem is a result in probability theory, mathematical statistics and statistical mechanics that gives necessary and sufficient conditions under which a strictly positive probability distribution (of events in a probability space) [clarification needed] can be represented as events generated by a Markov network (also known as a Markov random field).

  9. Memorylessness - Wikipedia

    en.wikipedia.org/wiki/Memorylessness

    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 ...