1
|
Journel L, Monmarché P. Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case. ESAIM-PROBAB STAT 2022. [DOI: 10.1051/ps/2021017] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
We establish the convergences (with respect to the simulation time t; the number of particles N; the timestep γ) of a Moran/Fleming-Viot type particle scheme toward the quasi-stationary distribution of a diffusion on the d-dimensional torus, killed at a smooth rate. In these conditions, quantitative bounds are obtained that, for each parameter (t →∞, N →∞ or γ → 0) are independent from the two others.
Collapse
|
2
|
Tough O, Nolen J. The Fleming-Viot process with McKean-Vlasov dynamics. ELECTRON J PROBAB 2022. [DOI: 10.1214/22-ejp820] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
3
|
Convergence of the Fleming-Viot process toward the minimal quasi-stationary distribution. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2021. [DOI: 10.30757/alea.v18-01] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
4
|
Mailler C, Villemonais D. Stochastic approximation on noncompact measure spaces and application to measure-valued Pólya processes. ANN APPL PROBAB 2020. [DOI: 10.1214/20-aap1561] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
|
5
|
Villemonais D. Lower Bound for the Coarse Ricci Curvature of Continuous-Time Pure-Jump Processes. J THEOR PROBAB 2020. [DOI: 10.1007/s10959-019-00918-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
6
|
Cérou F, Delyon B, Guyader A, Rousset M. A central limit theorem for Fleming–Viot particle systems. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2020. [DOI: 10.1214/19-aihp976] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
7
|
Del Moral P, Villemonais D. Exponential mixing properties for time inhomogeneous diffusion processes with killing. BERNOULLI 2018. [DOI: 10.3150/16-bej845] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
8
|
Central Limit Theorem for stationary Fleming-Viot particle systems in finite spaces. LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2018. [DOI: 10.30757/alea.v15-43] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
|
9
|
Chen ZQ, Fan WT(L. Systems of interacting diffusions with partial annihilation through membranes. ANN PROBAB 2017. [DOI: 10.1214/15-aop1047] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
10
|
Asselah A, Ferrari PA, Groisman P. Quasistationary Distributions and Fleming-Viot Processes in Finite Spaces. J Appl Probab 2016. [DOI: 10.1239/jap/1308662630] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
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.
Collapse
|
11
|
Abstract
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.
Collapse
|
12
|
Asselah A, Ferrari PA, Groisman P, Jonckheere M. Fleming–Viot selects the minimal quasi-stationary distribution: The Galton–Watson case. ANNALES DE L'INSTITUT HENRI POINCARÉ, PROBABILITÉS ET STATISTIQUES 2016. [DOI: 10.1214/14-aihp635] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
13
|
Villemonais D. Minimal quasi-stationary distribution approximation for a birth and death process. ELECTRON J PROBAB 2015. [DOI: 10.1214/ejp.v20-3482] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
14
|
Villemonais D. General approximation method for the distribution of Markov processes conditioned not to be killed. ESAIM-PROBAB STAT 2014. [DOI: 10.1051/ps/2013045] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
|
15
|
|
16
|
Méléard S, Villemonais D. Quasi-stationary distributions and population processes. PROBABILITY SURVEYS 2012. [DOI: 10.1214/11-ps191] [Citation(s) in RCA: 105] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
17
|
Villemonais D. Interacting Particle Systems and Yaglom Limit Approximation of Diffusions with Unbounded Drift. ELECTRON J PROBAB 2011. [DOI: 10.1214/ejp.v16-925] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
18
|
Grigorescu I, Kang M. Steady state and scaling limit for a traffic congestion model. ESAIM-PROBAB STAT 2010. [DOI: 10.1051/ps:2008029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
|
19
|
Ferrari P, Maric N. Quasi Stationary Distributions and Fleming-Viot Processes in Countable Spaces. ELECTRON J PROBAB 2007. [DOI: 10.1214/ejp.v12-415] [Citation(s) in RCA: 41] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
20
|
Grigorescu I, Kang M. Ergodic Properties of Multidimensional Brownian Motion with Rebirth. ELECTRON J PROBAB 2007. [DOI: 10.1214/ejp.v12-450] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
21
|
Burdzy K, Quastel J. An annihilating–branching particle model for the heat equation with average temperature zero. ANN PROBAB 2006. [DOI: 10.1214/009117906000000511] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
22
|
|