Search results
Results from the WOW.Com Content Network
If a Markov chain has a stationary distribution, then it can be converted to a measure-preserving dynamical system: Let the probability space be =, where is the set of all states for the Markov chain. Let the sigma-algebra on the probability space be generated by the cylinder sets.
Stationary distribution may refer to: . Discrete-time Markov chain § Stationary distributions and continuous-time Markov chain § Stationary distribution, a special distribution for a Markov chain such that if the chain starts with its stationary distribution, the marginal distribution of all states at any time will always be the stationary distribution.
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.
For a continuous time Markov chain (CTMC) with transition rate matrix, if can be found such that for every pair of states and = holds, then by summing over , the global balance equations are satisfied and is the stationary distribution of the process. [5]
In the mathematical theory of Markov chains, the Markov chain tree theorem is an expression for the stationary distribution of a Markov chain with finitely many states. It sums up terms for the rooted spanning trees of the Markov chain, with a positive combination for each tree.
the initial distribution of the process, i.e. the distribution of , is the stationary distribution, so that ,,, … are identically distributed. In the classic central limit theorem these random variables would be assumed to be independent , but here we have only the weaker assumption that the process has the Markov property ; and
In probability theory, the matrix analytic method is a technique to compute the stationary probability distribution of a Markov chain which has a repeating structure (after some point) and a state space which grows unboundedly in no more than one dimension.
Markov chose 20,000 letters from Pushkin’s Eugene Onegin, classified them into vowels and consonants, and counted the transition probabilities. The stationary distribution is 43.2 percent vowels and 56.8 percent consonants, which is close to the actual count in the book.