Search results
Results from the WOW.Com Content Network
In his first paper on Markov chains, published in 1906, Markov showed that under certain conditions the average outcomes of the Markov chain would converge to a fixed vector of values, so proving a weak law of large numbers without the independence assumption, [16] [17] [18] which had been commonly regarded as a requirement for such ...
A game of snakes and ladders or any other game whose moves are determined entirely by dice is a Markov chain, indeed, an absorbing Markov chain. This is in contrast to card games such as blackjack, where the cards represent a 'memory' of the past moves. To see the difference, consider the probability for a certain event in the game.
In probability theory, uniformization method, (also known as Jensen's method [1] or the randomization method [2]) is a method to compute transient solutions of finite state continuous-time Markov chains, by approximating the process by a discrete-time Markov chain. [2]
In statistics, Markov chain Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution.Given a probability distribution, one can construct a Markov chain whose elements' distribution approximates it – that is, the Markov chain's equilibrium distribution matches the target distribution.
A continuous-time Markov chain (CTMC) is a continuous stochastic process in which, for each state, the process will change state according to an exponential random variable and then move to a different state as specified by the probabilities of a stochastic matrix.
[1] [2] Such models are often described as M/G/1 type Markov chains because they can describe transitions in an M/G/1 queue. [3] [4] The method is a more complicated version of the matrix geometric method and is the classical solution method for M/G/1 chains. [5]
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 ...
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.