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Published: 8 June 2024

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1

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 1 (March 2000): 140–58. http://dx.doi.org/10.1239/aap/1013540027.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.
2

Hiraba, Seiji. "Jump-type Fleming-Viot processes." Advances in Applied Probability 32, no. 01 (March 2000): 140–58. http://dx.doi.org/10.1017/s0001867800009812.

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In 1991 Perkins [7] showed that the normalized critical binary branching process is a time inhomogeneous Fleming-Viot process. In the present paper we extend this result to jump-type branching processes and we show that the normalized jump-type branching processes are in a new class of probability measure-valued processes which will be called ‘jump-type Fleming-Viot processes’. Furthermore we also show that by using these processes it is possible to introduce another new class of measure-valued processes which are obtained by the combination of jump-type branching processes and Fleming-Viot processes.
3

Vaillancourt, Jean. "Interacting Fleming-Viot processes." Stochastic Processes and their Applications 36, no. 1 (October 1990): 45–57. http://dx.doi.org/10.1016/0304-4149(90)90041-p.

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4

XIANG, KAI-NAN, and TU-SHENG ZHANG. "SMALL TIME ASYMPTOTICS FOR FLEMING–VIOT PROCESSES." Infinite Dimensional Analysis, Quantum Probability and Related Topics 08, no. 04 (December 2005): 605–30. http://dx.doi.org/10.1142/s0219025705002177.

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In this paper, a sample path large deviation for Fleming–Viot processes corresponding to the small time asymptotics is established. The rate function is identified as the energy functional of paths associated to the Bhattacharya metric, the intrinsic metric of Fleming–Viot processes.
5

Feng, Shui, Byron Schmuland, Jean Vaillancourt, and Xiaowen Zhou. "Reversibility of Interacting Fleming–Viot Processes with Mutation, Selection, and Recombination." Canadian Journal of Mathematics 63, no. 1 (February 1, 2011): 104–22. http://dx.doi.org/10.4153/cjm-2010-071-1.

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Abstract Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies interacting with each other through migrations between the colonies. It is shown that reversibility fails when both migration and mutation are non-trivial.
6

Cloez, Bertrand, and Marie-Noémie Thai. "Fleming-Viot processes: two explicit examples." Latin American Journal of Probability and Mathematical Statistics 13, no. 1 (2016): 337. http://dx.doi.org/10.30757/alea.v13-14.

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7

Ethier, S. N., and Thomas G. Kurtz. "Fleming–Viot Processes in Population Genetics." SIAM Journal on Control and Optimization 31, no. 2 (March 1993): 345–86. http://dx.doi.org/10.1137/0331019.

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8

HE, HUI. "FLEMING–VIOT PROCESSES IN AN ENVIRONMENT." Infinite Dimensional Analysis, Quantum Probability and Related Topics 13, no. 03 (September 2010): 489–509. http://dx.doi.org/10.1142/s0219025710004127.

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We consider a new type of lookdown processes where spatial motion of each individual is influenced by an individual noise and a common noise, which could be regarded as an environment. Then a class of probability measure-valued processes on real line ℝ is constructed. The sample path properties are investigated: the values of this new type process are either purely atomic measures or absolutely continuous measures according to the existence of individual noise. When the process is absolutely continuous with respect to Lebesgue measure, we derive a new stochastic partial differential equation for the density process. At last we show that such processes also arise from normalizing a class of measure-valued branching diffusions in a Brownian medium as the classical result that Dawson–Watanabe superprocesses, conditioned to have total mass one, are Fleming–Viot superprocesses.
9

Ethier, S. N., and Stephen M. Krone. "Comparing Fleming-Viot and Dawson-Watanabe processes." Stochastic Processes and their Applications 60, no. 2 (December 1995): 171–90. http://dx.doi.org/10.1016/0304-4149(95)00056-9.

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10

Li, Zenghu, Tokuzo Shiga, and Lihua Yao. "A Reversibility Problem for Fleming-Viot Processes." Electronic Communications in Probability 4 (1999): 65–76. http://dx.doi.org/10.1214/ecp.v4-1007.

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11

Asselah, Amine, Pablo A. Ferrari, and Pablo Groisman. "Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces." Journal of Applied Probability 48, no. 02 (June 2011): 322–32. http://dx.doi.org/10.1017/s0021900200007907.

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Consider a continuous-time Markov process with transition rates matrixQin the state space Λ ⋃ {0}. In the associated Fleming-Viot processNparticles evolve independently in Λ with transition rates matrixQuntil one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges asN→ ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process withNparticles converges asN→ ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 /N.
12

Asselah, Amine, Pablo A. Ferrari, and Pablo Groisman. "Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces." Journal of Applied Probability 48, no. 2 (June 2011): 322–32. http://dx.doi.org/10.1239/jap/1308662630.

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Consider a continuous-time Markov process with transition rates matrix Q in the state space Λ ⋃ {0}. In the associated Fleming-Viot process N particles evolve independently in Λ with transition rates matrix Q until one of them attempts to jump to state 0. At this moment the particle jumps to one of the positions of the other particles, chosen uniformly at random. When Λ is finite, we show that the empirical distribution of the particles at a fixed time converges as N → ∞ to the distribution of a single particle at the same time conditioned on not touching {0}. Furthermore, the empirical profile of the unique invariant measure for the Fleming-Viot process with N particles converges as N → ∞ to the unique quasistationary distribution of the one-particle motion. A key element of the approach is to show that the two-particle correlations are of order 1 / N.
13

Kurtz, Thomas G., and S. N. Ethier. "Coupling and ergodic theorems for Fleming-Viot processes." Annals of Probability 26, no. 2 (April 1998): 533–61. http://dx.doi.org/10.1214/aop/1022855643.

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14

da Silva, Telles T., and Marcelo D. Fragoso. "A note on jump-type Fleming–Viot processes." Statistics & Probability Letters 76, no. 8 (April 2006): 821–30. http://dx.doi.org/10.1016/j.spl.2005.10.011.

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15

da Silva, Telles T., and Marcelo D. Fragoso. "Invariant measures for jump-type Fleming–Viot processes." Statistics & Probability Letters 76, no. 8 (April 2006): 796–802. http://dx.doi.org/10.1016/j.spl.2005.10.012.

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16

Li, QinFeng, ChunHua Ma, and KaiNan Xiang. "On strong Markov property for Fleming-Viot processes." Science China Mathematics 56, no. 10 (August 27, 2013): 2123–33. http://dx.doi.org/10.1007/s11425-013-4670-5.

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17

Schied, Alexander. "Geometric aspects of Fleming-Viot and Dawson-Watanabe processes." Annals of Probability 25, no. 3 (July 1997): 1160–79. http://dx.doi.org/10.1214/aop/1024404509.

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18

Vaillancourt, Jean. "On the scaling theorem for interacting Fleming-Viot processes." Stochastic Processes and their Applications 36, no. 2 (December 1990): 263–67. http://dx.doi.org/10.1016/0304-4149(90)90095-a.

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19

Birkner, Matthias, and Jochen Blath. "Generalised Stable Fleming-Viot Processes as Flickering Random Measures." Electronic Journal of Probability 14 (2009): 2418–37. http://dx.doi.org/10.1214/ejp.v14-712.

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20

Overbeck, Ludger, Michael Rockner, and Byron Schmuland. "An Analytic Approach to Fleming-Viot Processes with Interactive Selection." Annals of Probability 23, no. 1 (January 1995): 1–36. http://dx.doi.org/10.1214/aop/1176988374.

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21

Foucart, Clément. "Distinguished exchangeable coalescents and generalized Fleming-Viot processes with immigration." Advances in Applied Probability 43, no. 2 (June 2011): 348–74. http://dx.doi.org/10.1239/aap/1308662483.

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Coalescents with multiple collisions (also called Λ-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with immigration. Consider an infinite population with immigration labelled at each generation by N := {1, 2, …}. Some ancestral lineages cannot be followed backwards after some time because their ancestor is outside the population. The individuals with an immigrant ancestor constitute a distinguished family and we define exchangeable distinguished coalescent processes as a model for genealogy with immigration, focusing on simple distinguished coalescents, i.e. such that when a coagulation occurs all the blocks involved merge as a single block. These processes are characterized by two finite measures on [0, 1] denoted by M = (Λ0, Λ1). We call them M-coalescents. We show by martingale arguments that the condition of coming down from infinity for the M-coalescent coincides with that obtained by Schweinsberg for the Λ-coalescent. In the same vein as Bertoin and Le Gall, M-coalescents are associated with some stochastic flows. The superprocess embedded can be viewed as a generalized Fleming-Viot process with immigration. The measures Λ0 and Λ1 respectively specify the reproduction and the immigration. The coming down from infinity of the M-coalescent will be interpreted as the initial types extinction: after a certain time all individuals are immigrant children.
22

Foucart, Clément. "Distinguished exchangeable coalescents and generalized Fleming-Viot processes with immigration." Advances in Applied Probability 43, no. 02 (June 2011): 348–74. http://dx.doi.org/10.1017/s0001867800004894.

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Coalescents with multiple collisions (also called Λ-coalescents or simple exchangeable coalescents) are used as models of genealogies. We study a new class of Markovian coalescent processes connected to a population model with immigration. Consider an infinite population with immigration labelled at each generation byN:= {1, 2, …}. Some ancestral lineages cannot be followed backwards after some time because their ancestor is outside the population. The individuals with an immigrant ancestor constitute a distinguished family and we define exchangeable distinguished coalescent processes as a model for genealogy with immigration, focusing on simple distinguished coalescents, i.e. such that when a coagulation occurs all the blocks involved merge as a single block. These processes are characterized by two finite measures on [0, 1] denoted byM= (Λ0, Λ1). We call themM-coalescents. We show by martingale arguments that the condition of coming down from infinity for theM-coalescent coincides with that obtained by Schweinsberg for the Λ-coalescent. In the same vein as Bertoin and Le Gall,M-coalescents are associated with some stochastic flows. The superprocess embedded can be viewed as a generalized Fleming-Viot process with immigration. The measures Λ0and Λ1respectively specify the reproduction and the immigration. The coming down from infinity of theM-coalescent will be interpreted as the initial types extinction: after a certain time all individuals are immigrant children.
23

Gonzalez Casanova, Adrian, and Charline Smadi. "On Λ-Fleming–Viot processes with general frequency-dependent selection." Journal of Applied Probability 57, no. 4 (November 23, 2020): 1162–97. http://dx.doi.org/10.1017/jpr.2020.55.

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AbstractWe construct a multitype constant-size population model allowing for general selective interactions as well as extreme reproductive events. Our multidimensional model aims for the generality of adaptive dynamics and the tractability of population genetics. It generalises the idea of Krone and Neuhauser [39] and González Casanova and Spanò [29], who represented the selection by allowing individuals to sample several potential parents in the previous generation before choosing the ‘strongest’ one, by allowing individuals to use any rule to choose their parent. The type of the newborn can even not be one of the types of the potential parents, which allows modelling mutations. Via a large population limit, we obtain a generalisation of $\Lambda$ -Fleming–Viot processes, with a diffusion term and a general frequency-dependent selection, which allows for non-transitive interactions between the different types present in the population. We provide some properties of these processes related to extinction and fixation events, and give conditions for them to be realised as unique strong solutions of multidimensional stochastic differential equations with jumps. Finally, we illustrate the generality of our model with applications to some classical biological interactions. This framework provides a natural bridge between two of the most prominent modelling frameworks of biological evolution: population genetics and eco-evolutionary models.
24

Ethier, S. N., and Thomas G. Kurtz. "Convergence to Fleming-Viot processes in the weak atomic topology." Stochastic Processes and their Applications 54, no. 1 (November 1994): 1–27. http://dx.doi.org/10.1016/0304-4149(94)00006-9.

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25

Ferrari, Pablo, and Nevena Maric. "Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces." Electronic Journal of Probability 12 (2007): 684–702. http://dx.doi.org/10.1214/ejp.v12-415.

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26

Donnelly, Peter, and Thomas G. Kurtz. "Genealogical processes for Fleming-Viot models with selection and recombination." Annals of Applied Probability 9, no. 4 (November 1999): 1091–148. http://dx.doi.org/10.1214/aoap/1029962866.

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27

Handa, Kenji. "Stationary distributions for a class of generalized Fleming–Viot processes." Annals of Probability 42, no. 3 (May 2014): 1257–84. http://dx.doi.org/10.1214/12-aop829.

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28

Berestycki, J., L. Döring, L. Mytnik, and L. Zambotti. "On exceptional times for generalized Fleming–Viot processes with mutations." Stochastic Partial Differential Equations: Analysis and Computations 2, no. 1 (March 2014): 84–120. http://dx.doi.org/10.1007/s40072-014-0026-6.

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29

Röckner, Michael, and Byron Schmuland. "Quasi-Regular Dirichlet Forms: Examples and Counterexamples." Canadian Journal of Mathematics 47, no. 1 (February 1, 1995): 165–200. http://dx.doi.org/10.4153/cjm-1995-009-3.

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AbstractWe prove some new results on quasi-regular Dirichlet forms. These include results on perturbations of Dirichlet forms, change of speed measure, and tightness. The tightness implies the existence of an associated right continuous strong Markov process. We also discuss applications to a number of examples including cases with possibly degenerate (sub)-elliptic part, diffusions on loop spaces, and certain Fleming- Viot processes.
30

Dawson, Donald A., Andreas Greven, and Jean Vaillancourt. "Equilibria and quasiequilibria for infinite collections of interacting Fleming-Viot processes." Transactions of the American Mathematical Society 347, no. 7 (July 1, 1995): 2277–360. http://dx.doi.org/10.1090/s0002-9947-1995-1297523-5.

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31

Chen, Yu-Ting, and J. Theodore Cox. "Weak atomic convergence of finite voter models toward Fleming–Viot processes." Stochastic Processes and their Applications 128, no. 7 (July 2018): 2463–88. http://dx.doi.org/10.1016/j.spa.2017.09.015.

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32

Liu, Huili, and Xiaowen Zhou. "Some support properties for a class of ${\varLambda}$-Fleming–Viot processes." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 51, no. 3 (August 2015): 1076–101. http://dx.doi.org/10.1214/13-aihp598.

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33

Feng, Shui, and Feng-Yu Wang. "A Class of Infinite-Dimensional Diffusion Processes with Connection to Population Genetics." Journal of Applied Probability 44, no. 4 (December 2007): 938–49. http://dx.doi.org/10.1239/jap/1197908815.

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Starting from a sequence of independent Wright-Fisher diffusion processes on [0, 1], we construct a class of reversible infinite-dimensional diffusion processes on Δ∞ := {x ∈ [0, 1]N: ∑i≥1xi = 1} with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence of the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space S. This provides a reasonable alternative to the Fleming-Viot process, which does not satisfy the log-Sobolev inequality when S is infinite as observed by Stannat (2000).
34

Dawson, Donald A., Andreas Greven, and Jean Vaillancourt. "Equilibria and Quasi-Equilibria for Infinite Collections of Interacting Fleming-Viot Processes." Transactions of the American Mathematical Society 347, no. 7 (July 1995): 2277. http://dx.doi.org/10.2307/2154827.

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35

da Silva, Telles Timóteo, and Marcelo D. Fragoso. "Sample paths of jump-type Fleming–Viot processes with bounded mutation operators." Statistics & Probability Letters 78, no. 13 (September 2008): 1784–91. http://dx.doi.org/10.1016/j.spl.2008.01.033.

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36

Cerrai, Sandra, and Philippe Clément. "On a class of degenerate elliptic operators arising from Fleming-Viot processes." Journal of Evolution Equations 1, no. 3 (September 2001): 243–76. http://dx.doi.org/10.1007/pl00001370.

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37

Feng, Shui, and Feng-Yu Wang. "A Class of Infinite-Dimensional Diffusion Processes with Connection to Population Genetics." Journal of Applied Probability 44, no. 04 (December 2007): 938–49. http://dx.doi.org/10.1017/s0021900200003648.

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Starting from a sequence of independent Wright-Fisher diffusion processes on [0, 1], we construct a class of reversible infinite-dimensional diffusion processes on Δ∞ := { x ∈ [0, 1] N : ∑ i≥1 x i = 1} with GEM distribution as the reversible measure. Log-Sobolev inequalities are established for these diffusions, which lead to the exponential convergence of the corresponding reversible measures in the entropy. Extensions are made to a class of measure-valued processes over an abstract space S. This provides a reasonable alternative to the Fleming-Viot process, which does not satisfy the log-Sobolev inequality when S is infinite as observed by Stannat (2000).
38

Li, Zenghu, Huili Liu, Jie Xiong, and Xiaowen Zhou. "The reversibility and an SPDE for the generalized Fleming–Viot processes with mutation." Stochastic Processes and their Applications 123, no. 12 (December 2013): 4129–55. http://dx.doi.org/10.1016/j.spa.2013.06.013.

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39

Kouritzin, Michael A., and Khoa Lê. "Long-time limits and occupation times for stable Fleming–Viot processes with decaying sampling rates." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 56, no. 4 (November 2020): 2595–620. http://dx.doi.org/10.1214/20-aihp1051.

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40

Achaz, Guillaume, Amaury Lambert, and Emmanuel Schertzer. "The sequential loss of allelic diversity." Advances in Applied Probability 50, A (December 2018): 13–29. http://dx.doi.org/10.1017/apr.2018.67.

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Abstract In this paper we give a new flavour to what Peter Jagers and his co-authors call `the path to extinction'. In a neutral population of constant size N, assume that each individual at time 0 carries a distinct type, or allele. Consider the joint dynamics of these N alleles, for example the dynamics of their respective frequencies and more plainly the nonincreasing process counting the number of alleles remaining by time t. Call this process the extinction process. We show that in the Moran model, the extinction process is distributed as the process counting (in backward time) the number of common ancestors to the whole population, also known as the block counting process of the N-Kingman coalescent. Stimulated by this result, we investigate whether it extends (i) to an identity between the frequencies of blocks in the Kingman coalescent and the frequencies of alleles in the extinction process, both evaluated at jump times, and (ii) to the general case of Λ-Fleming‒Viot processes.
41

Albanese, Angela A., and Elisabetta M. Mangino. "Analyticity of a class of degenerate evolution equations on the canonical simplex of Rd arising from Fleming–Viot processes." Journal of Mathematical Analysis and Applications 379, no. 1 (July 2011): 401–24. http://dx.doi.org/10.1016/j.jmaa.2011.01.015.

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42

Gufler, Stephan. "Pathwise construction of tree-valued Fleming-Viot processes." Electronic Journal of Probability 23 (2018). http://dx.doi.org/10.1214/18-ejp166.

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43

Hughes, Thomas, and Xiaowen Zhou. "Instantaneous support propagation for Λ-Fleming–Viot processes." Stochastic Processes and their Applications, November 2022. http://dx.doi.org/10.1016/j.spa.2022.10.009.

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44

Ascolani, Filippo, Antonio Lijoi, and Matteo Ruggiero. "Predictive inference with Fleming–Viot-driven dependent Dirichlet processes." Bayesian Analysis, April 2020. http://dx.doi.org/10.1214/20-ba1206.

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45

Forman, Noah, Soumik Pal, Douglas Rizzolo, and Matthias Winkel. "Ranked masses in two-parameter Fleming–Viot diffusions." Transactions of the American Mathematical Society, October 28, 2022. http://dx.doi.org/10.1090/tran/8764.

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Previous work constructed Fleming–Viot-type measure-valued diffusions (and diffusions on a space of interval partitions of the unit interval [ 0 , 1 ] [0,1] ) that are stationary with respect to the Poisson–Dirichlet random measures with parameters α ∈ ( 0 , 1 ) \alpha \in (0,1) and θ > − α \theta > -\alpha . In this paper, we complete the proof that these processes resolve a conjecture by Feng and Sun [Probab. Theory Related Fields 148 (2010), pp. 501–525] by showing that the processes of ranked atom sizes (or of ranked interval lengths) of these diffusions are members of a two-parameter family of diffusions introduced by Petrov [Funct. Anal. Appl. 43 (2009), pp. 279–296], extending a model by Ethier and Kurtz [Adv. in Appl. Probab. 13 (1981), pp. 429–452] in the case α = 0 \alpha =0 .
46

OVERBECK, Ludger, and Michael RÖCKNER. "Geometric aspects of finite and infinite-dimensional Fleming-Viot processes." Random Operators and Stochastic Equations 5, no. 1 (1997). http://dx.doi.org/10.1515/rose.1997.5.1.35.

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47

"Measure valued diffusion processes associated with stochastic processes of Fleming-Viot type." Stochastic Processes and their Applications 21, no. 1 (December 1985): 26. http://dx.doi.org/10.1016/0304-4149(85)90273-x.

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48

Foucart, Clément, and Olivier Hénard. "Stable continuous-state branching processes with immigration and Beta-Fleming-Viot processes with immigration." Electronic Journal of Probability 18 (2013). http://dx.doi.org/10.1214/ejp.v18-2024.

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49

Labbé, Cyril. "From flows of $\Lambda$-Fleming-Viot processes to lookdown processes via flows of partitions." Electronic Journal of Probability 19 (2014). http://dx.doi.org/10.1214/ejp.v19-3192.

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50

Gufler, Stephan. "A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes." Electronic Journal of Probability 23 (2018). http://dx.doi.org/10.1214/18-ejp153.

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