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