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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 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 ...

  4. 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.

  5. Renewal theory - Wikipedia

    en.wikipedia.org/wiki/Renewal_theory

    The Poisson process is the unique renewal process with the Markov property, [1] ... (PDF). Transactions of the American Mathematical Society. 63 (3): 422–438.

  6. 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.

  7. Random field - Wikipedia

    en.wikipedia.org/wiki/Random_field

    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.

  8. 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.

  9. Lumpability - Wikipedia

    en.wikipedia.org/wiki/Lumpability

    Download as PDF; Printable version ... lumpability is a method for reducing the size of the state space of some continuous-time Markov ... a property whereby a small ...