Search results
Results from the WOW.Com Content Network
D. G. Champernowne built a Markov chain model of the distribution of income in 1953. [93] Herbert A. Simon and co-author Charles Bonini used a Markov chain model to derive a stationary Yule distribution of firm sizes. [94] Louis Bachelier was the first to observe that stock prices followed a random walk. [95]
In probability theory, Kelly's lemma states that for a stationary continuous-time Markov chain, a process defined as the time-reversed process has the same stationary distribution as the forward-time process. [1] The theorem is named after Frank Kelly. [2] [3] [4] [5]
Stationary distribution [ edit ] The number of jobs in the queue can be written as M/G/1 type Markov chain and the stationary distribution found for state i (written π i ) in the case D = 1 to be [ 4 ]
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.
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]
Among Markov chain Monte Carlo (MCMC) algorithms, coupling from the past is a method for sampling from the stationary distribution of a Markov chain. Contrary to many MCMC algorithms, coupling from the past gives in principle a perfect sample from the stationary distribution. It was invented by James Propp and David Wilson in 1996.
Markov chains with generator matrices or block matrices of this form are called M/G/1 type Markov chains, [13] a term coined by Marcel F. Neuts. [ 14 ] [ 15 ] An M/G/1 queue has a stationary distribution if and only if the traffic intensity ρ = λ E ( G ) {\displaystyle \rho =\lambda \mathbb {E} (G)} is less than 1, in which case the unique ...
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 ...