Fleming-Viot process
Encyclopedia
In probability theory
, a Fleming–Viot process (F–V process) is a member of a particular subset of probability-measure valued Markov process
es on compact
metric space
s, as defined in the 1979 paper by Wendell Helms Fleming and Michel Viot. Such processes are martingales
and diffusions
.
The Fleming–Viot processes have proved to be important to the development of a mathematical basis for the theories behind allele drift.
They are generalisations of the Wright-Fisher process and arise as infinite population limits of suitably rescaled variants of Moran processes
.
Probability theory
Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single...
, a Fleming–Viot process (F–V process) is a member of a particular subset of probability-measure valued Markov process
Markov process
In probability theory and statistics, a Markov process, named after the Russian mathematician Andrey Markov, is a time-varying random phenomenon for which a specific property holds...
es on compact
Compact space
In mathematics, specifically general topology and metric topology, a compact space is an abstract mathematical space whose topology has the compactness property, which has many important implications not valid in general spaces...
metric space
Metric space
In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space...
s, as defined in the 1979 paper by Wendell Helms Fleming and Michel Viot. Such processes are martingales
Martingale (probability theory)
In probability theory, a martingale is a model of a fair game where no knowledge of past events can help to predict future winnings. In particular, a martingale is a sequence of random variables for which, at a particular time in the realized sequence, the expectation of the next value in the...
and diffusions
Diffusion process
In probability theory, a branch of mathematics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with continuous sample paths....
.
The Fleming–Viot processes have proved to be important to the development of a mathematical basis for the theories behind allele drift.
They are generalisations of the Wright-Fisher process and arise as infinite population limits of suitably rescaled variants of Moran processes
Moran process
A Moran process, named after Patrick Moran, is a stochastic process used in biology to describe finite populations. It can be used to model variety-increasing processes such as mutation as well as variety-reducing effects such as genetic drift and natural selection...
.