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  2. 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 ...

  3. Markov property - Wikipedia

    en.wikipedia.org/wiki/Markov_property

    The term Markov assumption is used to describe a model where the Markov property is assumed to hold, such as a hidden Markov model. A Markov random field extends this property to two or more dimensions or to random variables defined for an interconnected network of items. [1] An example of a model for such a field is the Ising model.

  4. P versus NP problem - Wikipedia

    en.wikipedia.org/wiki/P_versus_NP_problem

    In other words, any problem in EXPTIME is solvable by a deterministic Turing machine in O(2 p(n)) time, where p(n) is a polynomial function of n. A decision problem is EXPTIME-complete if it is in EXPTIME, and every problem in EXPTIME has a polynomial-time many-one reduction to it. A number of problems are known to be EXPTIME-complete.

  5. Markovian arrival process - Wikipedia

    en.wikipedia.org/wiki/Markovian_arrival_process

    The simplest example is a Poisson process where D 0 = −λ and D 1 = λ where there is only one possible transition, it is observable, and occurs at rate λ. For Q to be a valid transition rate matrix, the following restrictions apply to the D i

  6. Information theory - Wikipedia

    en.wikipedia.org/wiki/Information_theory

    A memoryless source is one in which each message is an independent identically distributed random variable, whereas the properties of ergodicity and stationarity impose less restrictive constraints. All such sources are stochastic. These terms are well studied in their own right outside information theory.

  7. 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 ...

  8. Geometric distribution - Wikipedia

    en.wikipedia.org/wiki/Geometric_distribution

    The geometric distribution is the only memoryless discrete probability distribution. [4] It is the discrete version of the same property found in the exponential distribution. [1]: 228 The property asserts that the number of previously failed trials does not affect the number of future trials needed for a success.

  9. Markov decision process - Wikipedia

    en.wikipedia.org/wiki/Markov_decision_process

    Markov decision process (MDP), also called a stochastic dynamic program or stochastic control problem, is a model for sequential decision making when outcomes are uncertain. [ 1 ] Originating from operations research in the 1950s, [ 2 ] [ 3 ] MDPs have since gained recognition in a variety of fields, including ecology , economics , healthcare ...

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