For 10 points, what is this stochastic process, named for a Russian mathematician, in which the future value of a variable is independent of its past history?
The stability of the continuous parameter type can be determined by Foster-Lyapunov criteria, and the application of Dynkin's formula can demonstrate that they are Harris recurrent. If it is possible to go from each state to every other state, then they are ergodic, and the rate at which they converge to a stationary distribution is the mixing rate. Ehrenfest, Bernoulli and Laplace used them to develop discrete models for the exchange of gas molecules between two containers. The Gibbs sampler is an example of the Monte Carlo type of this process, that simulates direct draws from a complex distribution of interest. For 10 points, what is this stochastic process, named for a Russian mathematician, in which the future value of a variable is independent of its past history?
The stability of the continuous parameter type can be determined by Foster-Lyapunov criteria, and the application of Dynkin's formula can demonstrate that they are Harris recurrent.
{Markov chain} or {Markov} process [prompt on {stochastic}]