Stochastic Processes
A formal definition of time-reversibility is stated by Tong in the context of time-series. In general, a Gaussian process is time-reversible. The process defined by a time-series model which represents values as a linear combination of past values and of present and past innovations (see Autoregressive moving average model) is, except for limited special cases, not time-reversible unless the innovations have a normal distribution (in which case the model is a Gaussian process).
A stationary Markov Chain is reversible if the transition matrix {pij} and the stationary distribution {πj} satisfy
for all i and j. Such Markov Chains provide examples of stochastic processes which are time-reversible but non-Gaussian.
Time reversal of numerous classes of stochastic processes have been studied including Lévy processes stochastic networks (Kelly's lemma) birth and death processes Markov chains and piecewise deterministic Markov processes.
Read more about this topic: Time Reversibility
Famous quotes containing the word processes:
“The higher processes are all processes of simplification. The novelist must learn to write, and then he must unlearn it; just as the modern painter learns to draw, and then learns when utterly to disregard his accomplishment, when to subordinate it to a higher and truer effect.”
—Willa Cather (1873–1947)