In
probability theory
Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set ...
, a Fleming–Viot process (F–V process) is a member of a particular subset of
probability measure-valued
Markov process
A Markov chain or Markov process is a stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happe ...
es on
compact
Compact as used in politics may refer broadly to a pact or treaty; in more specific cases it may refer to:
* Interstate compact
* Blood compact, an ancient ritual of the Philippines
* Compact government, a type of colonial rule utilized in British ...
metric space
In mathematics, a metric space is a set together with a notion of '' distance'' between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general set ...
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.
See also
*
Coalescent theory
*
Voter model
In the mathematical theory of probability, the voter model is an interacting particle system introduced by Richard A. Holley and Thomas M. Liggett in 1975.
One can imagine that there is a "voter" at each point on a connected graph, where the c ...
References
*Fleming, W. H., Michel Viot, M. (1979
"Some measure-valued Markov processes in population genetics theory" (PDF format)''Indiana University Mathematics Journal'', 28 (5), 817–843.
*Ferrari, Pablo A.; Mari, Nevena
"Quasi stationary distributions and Fleming Viot processes", Lecture presentation
*
Markov processes
Statistical genetics
Martingale theory
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