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Markov's principle (also known as the Leningrad principle [1]), named after Andrey Markov Jr, is a conditional existence statement for which there are many equivalent formulations, as discussed below. The principle is logically valid classically, but not in intuitionistic constructive mathematics. However, many particular instances of it are ...
Markov's inequality (and other similar inequalities) relate probabilities to expectations, and provide (frequently loose but still useful) bounds for the cumulative distribution function of a random variable. Markov's inequality can also be used to upper bound the expectation of a non-negative random variable in terms of its distribution function.
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.
With this, one may validate Markov's principle and the extended Church's principle (and a second-order variant thereof), which come down to simple statement about object such as or (+). These imply C T 0 {\displaystyle {\mathrm {CT} }_{0}} and independence of premise I P 0 {\displaystyle {\mathrm {IP} }_{0}} .
A Markov perfect equilibrium is an equilibrium concept in game theory. It has been used in analyses of industrial organization , macroeconomics , and political economy . It is a refinement of the concept of subgame perfect equilibrium to extensive form games for which a pay-off relevant state space can be identified.
The Markov-modulated Poisson process or MMPP where m Poisson processes are switched between by an underlying continuous-time Markov chain. [8] If each of the m Poisson processes has rate λ i and the modulating continuous-time Markov has m × m transition rate matrix R , then the MAP representation is
The Kolmogorov backward equation (KBE) (diffusion) and its adjoint sometimes known as the Kolmogorov forward equation (diffusion) are partial differential equations (PDE) that arise in the theory of continuous-time continuous-state Markov processes. Both were published by Andrey Kolmogorov in 1931. [1]
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