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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 .
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.
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 ...
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.
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 ...
Then we can apply the strong Markov property to deduce that a relative path subsequent to , given by := (+), is also simple Brownian motion independent of . Then the probability distribution for the last time W ( s ) {\displaystyle W(s)} is at or above the threshold a {\displaystyle a} in the time interval [ 0 , t ] {\displaystyle [0,t]} can be ...
A Markov chain with two states, A and E. In probability, a discrete-time Markov chain (DTMC) is a sequence of random variables, known as a stochastic process, in which the value of the next variable depends only on the value of the current variable, and not any variables in the past.
A Markov number or Markoff number is a positive integer x, y or z that is part of a solution to the Markov Diophantine equation + + =, studied by Andrey Markoff (1879, 1880).. The first few Markov numbers are