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Fleming–Viot process

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Inprobability theory, aFleming–Viot process (F–V process) is a member of a particular subset ofprobability measure-valuedMarkov processes oncompact metric spaces, as defined in the 1979 paper byWendell Helms Fleming and Michel Viot. Such processes aremartingales anddiffusions.

The Fleming–Viot processes have proved to be important to the development of a mathematical basis for the theories behindallele drift.They are generalisations of the Wright–Fisher process and arise as infinite population limits of suitably rescaled variants ofMoran processes.

References

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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"Archived 2016-03-03 at theWayback Machine, Lecture presentation
Asselah, A.; Ferrari, P. A.; Groisman, P. (2011). "Quasistationary distributions and Fleming-Viot processes in finite spaces".Journal of Applied Probability.48 (2): 322.arXiv:0904.3039.doi:10.1239/jap/1308662630.S2CID 7206192.

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Discrete time	Bernoulli process Branching process Chinese restaurant process Galton–Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding Biased Maximal entropy
Continuous time	Additive process Airy process Bessel process Birth–death process pure birth Brownian motion Bridge Dyson Excursion Fractional Geometric Meander Cauchy process Contact process Continuous-time random walk Cox process Diffusion process Empirical process Feller process Fleming–Viot process Gamma process Geometric process Hawkes process Hunt process Interacting particle systems Itô diffusion Itô process Jump diffusion Jump process Lévy process Local time Markov additive process McKean–Vlasov process Ornstein–Uhlenbeck process Poisson process Compound Non-homogeneous Quasimartingale Schramm–Loewner evolution Semimartingale Sigma-martingale Stable process Superprocess Telegraph process Variance gamma process Wiener process Wiener sausage
Both	Branching process Gaussian process Hidden Markov model (HMM) Markov process Martingale Differences Local Sub- Super- Random dynamical system Regenerative process Renewal process Stochastic chains with memory of variable length White noise
Fields and other	Dirichlet process Gaussian random field Gibbs measure Hopfield model Ising model Potts model Boolean network Markov random field Percolation Pitman–Yor process Point process Cox Determinantal Poisson Random field Random graph
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Financial models	Binomial options pricing model Black–Derman–Toy Black–Karasinski Black–Scholes Chan–Karolyi–Longstaff–Sanders (CKLS) Chen Constant elasticity of variance (CEV) Cox–Ingersoll–Ross (CIR) Garman–Kohlhagen Heath–Jarrow–Morton (HJM) Heston Ho–Lee Hull–White Korn-Kreer-Lenssen LIBOR market Rendleman–Bartter SABR volatility Vašíček Wilkie
Actuarial models	Bühlmann Cramér–Lundberg Risk process Sparre–Anderson
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Properties	Càdlàg paths Continuous Continuous paths Ergodic Exchangeable Feller-continuous Gauss–Markov Markov Mixing Piecewise-deterministic Predictable Progressively measurable Self-similar Stationary Time-reversible
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Inequalities	Burkholder–Davis–Gundy Doob's martingale Doob's upcrossing Kunita–Watanabe Marcinkiewicz–Zygmund
Tools	Cameron–Martin formula Convergence of random variables Doléans-Dade exponential Doob decomposition theorem Doob–Meyer decomposition theorem Doob's optional stopping theorem Dynkin's formula Feynman–Kac formula Filtration Girsanov theorem Infinitesimal generator Itô integral Itô's lemma Karhunen–Loève theorem Kolmogorov continuity theorem Kolmogorov extension theorem Lévy–Prokhorov metric Malliavin calculus Martingale representation theorem Optional stopping theorem Prokhorov's theorem Quadratic variation Reflection principle Skorokhod integral Skorokhod's representation theorem Skorokhod space Snell envelope Stochastic differential equation Tanaka Stopping time Stratonovich integral Uniform integrability Usual hypotheses Wiener space Classical Abstract
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