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One method of finding the stationary probability distribution, π, of an ergodic continuous-time Markov chain, Q, is by first finding its embedded Markov chain (EMC). Strictly speaking, the EMC is a regular discrete-time Markov chain, sometimes referred to as a jump process.
The mixing time of a Markov chain is the number of steps needed for this convergence to happen, to a suitable degree of accuracy. A family of Markov chains is said to be rapidly mixing if the mixing time is a polynomial function of some size parameter of the Markov chain, and slowly mixing otherwise. This book is about finite Markov chains ...
MCMC methods can be described in three steps: first using a stochastic mechanism a new state for the Markov chain is proposed. Secondly, the probability of this new state to be correct is calculated. Thirdly, a new random variable (0,1) is proposed.
A basic property about an absorbing Markov chain is the expected number of visits to a transient state j starting from a transient state i (before being absorbed). This can be established to be given by the (i, j) entry of so-called fundamental matrix N, obtained by summing Q k for all k (from 0 to ∞).
This category is for articles about the theory of Markov chains and processes, and associated processes. See Category:Markov models for models for specific applications that make use of Markov processes.
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. An equivalent formulation describes the process as changing state according to ...
Every adapted right continuous Feller process on a filtered probability space (,, ()) satisfies the strong Markov property with respect to the filtration (+), i.e., for each (+)-stopping time, conditioned on the event {<}, we have that for each , + is independent of + given .
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.