Open Access
Volume 27, 2023
Page(s) 278 - 323
Published online 15 February 2023
  1. Y. Bakhtin and J.C. Mattingly, Stationary solutions of stochastic differential equations with memory and stochastic partial differential equations. Commun. Contemp. Math. 7 (2005) 553–582. [CrossRef] [Google Scholar]
  2. J.-B. Bardet, A. Christen, A. Guillin, F. Malrieu and P.-A. Zitt, Total variation estimates for the TCP process. Electr. J. Probab. 18 (2013) 21. [Google Scholar]
  3. D.P. Bertsekas and S.E. Shreve, Stochastic optimal control. Vol. 139 of Mathematics in Science and Engineering. Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London (1978), the discrete time case. [Google Scholar]
  4. J. Bierkens, P. Fearnhead and G. Roberts, The zig–zag process and super-efficient sampling for Bayesian analysis of big data. Ann. Statist. 47 (2019) 1288–1320. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. Bierkens, G. Roberts and P.-A. Zitt, Ergodicity of the zigzag process. Ann. Appl. Probab. 29 (2019) 2266–2301. [CrossRef] [MathSciNet] [Google Scholar]
  6. V.S. Borkar and R. Sundaresan, Asymptotics of the invariant measure in mean field models with jumps. Stoch. Syst. 2 (2012) 322–380. [CrossRef] [MathSciNet] [Google Scholar]
  7. N. Bou-Rabee and M. Hairer, Nonasymptotic mixing of the MALA algorithm. IMA J. Numer. Anal. 33 (2013) 80–110. [CrossRef] [MathSciNet] [Google Scholar]
  8. N. Brosse, A. Durmus, É. Moulines and S. Sabanis, The tamed unadjusted Langevin algorithm. Stoch. Process. Appl. 129 (2019) 3638–3663. [CrossRef] [Google Scholar]
  9. V. Calvez, G. Raoul and C. Schmeiser, Confinement by biased velocity jumps: aggregation of Escherichia coli. Kinet. Relat. Models 8 (2015) 651–666. [CrossRef] [MathSciNet] [Google Scholar]
  10. J.A. Cañizo and H. Yoldaş, Asymptotic behaviour of neuron population models structured by elapsed-time. Nonlinearity 32 (2019) 464–495. [CrossRef] [MathSciNet] [Google Scholar]
  11. P. Cattiaux, A. Guillin and F. Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case. Probab. Theory Related Fields 140 (2008) 19–40. [CrossRef] [MathSciNet] [Google Scholar]
  12. F. Cérou and A. Guyader, Adaptive multilevel splitting for rare event analysis. Stoch. Anal. Appl. 25 (2007) 417–443. [CrossRef] [MathSciNet] [Google Scholar]
  13. D. Chafaï, F. Malrieu and K. Paroux, On the long time behavior of the TCP window size process. Stoch. Process. Appl. 120 (2010) 1518–1534. [CrossRef] [Google Scholar]
  14. B. Cloez and M.-N. Thai, Quantitative results for the Fleming-Viot particle system and quasi-stationary distributions in discrete space. Stoch. Process. Appl. 126 (2016) 680–702. [CrossRef] [Google Scholar]
  15. M. Davis, Markov Models and Optimization, Monographs on Statistics and Applied Probability. Chapman and Hall (1993). [Google Scholar]
  16. P. Del Moral, Mean field simulation for Monte Carlo integration. Vol. 126 of Monographs on Statistics and Applied Probability. CRC Press, Boca Raton, FL (2013). [Google Scholar]
  17. P. Del Moral and L. Miclo, Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering, in Séminaire de Probabilités, XXXIV. Vol. 1729 of Lecture Notes in Math. Springer, Berlin (2000), pp. 1–145. 10.1007/BFb0103798. [Google Scholar]
  18. R. Dumitrescu, B. Øksendal and A. Sulem, Stochastic control of mean-field SPDEs with jumps. J. Optim. Theory Appl. 176 (2018) 176–559. [CrossRef] [MathSciNet] [Google Scholar]
  19. T.E. Duncan and H. Tembine, Linear-quadratic mean-field-type games: a direct Method. Games 9 (2018) Paper No. 7, 18. [CrossRef] [Google Scholar]
  20. A. Durmus, A. Eberle, A. Guillin and R. Zimmer, An elementary approach to uniform in time propagation of chaos. Proc. Am. Math. Soc. 148 (2020) 5387–5398. [CrossRef] [Google Scholar]
  21. A. Durmus, A. Guillin and P. Monmarché, Geometric ergodicity of the Bouncy Particle Sampler. Ann. Appl. Probab. 30 (2020) 2069–2098. [CrossRef] [MathSciNet] [Google Scholar]
  22. A. Durmus, A. Guillin and P. Monmarché, Piecewise deterministic Markov processes and their invariant measures. Ann. l'Inst. Henri Poincaré, Probab. Stat. 57 (2021) 1442–1475. [MathSciNet] [Google Scholar]
  23. A. Durmus, S. Majewski and B. Miasojedow, Analysis of Langevin Monte-Carlo via convex optimization. J. Mach. Learn. Res. 20 (2019) 1–46. [Google Scholar]
  24. A. Eberle, Reflection couplings and contraction rates for diffusions. Probab. Theory Related Fields 166 (2016) 851–886. [CrossRef] [MathSciNet] [Google Scholar]
  25. A. Eberle and R. Zimmer, Sticky couplings of multidimensional diffusions with different drifts. Ann. l'Inst. Henri Poincaré, Probab. Stat. 55 (2019) 2370–2394. [MathSciNet] [Google Scholar]
  26. R. Erban and H.G. Othmer, From individual to collective behavior in bacterial chemotaxis. SIAM J. Appl. Math. 65 (2004/05) 361–391. [CrossRef] [MathSciNet] [Google Scholar]
  27. N. Fétique, Long-time behaviour of generalised Zig-Zag process. ArXiv e-prints arXiv:1710.01087 (2017). [Google Scholar]
  28. W.H. Fleming and M. Viot, Some measure-valued Markov processes in population genetics theory. Indiana Univ. Math. J. 28 (1979) 817–843. [CrossRef] [MathSciNet] [Google Scholar]
  29. J. Fontbona, H. Guérin and F. Malrieu, Long time behavior of telegraph processes under convex potentials. Stoch. Process. Appl. 126 (2016) 3077–3101. [CrossRef] [Google Scholar]
  30. M. Hairer and J.C. Mattingly, Yet another look at Harris’ ergodic theorem for Markov chains, in Seminar on Stochastic Analysis, Random Fields and Applications VI. Vol. 63 of Progr. Probab.. Birkhäuser/Springer Basel AG, Basel (2011), pp. 109–117. [Google Scholar]
  31. L. Journel and P. Monmarché, Convergence of a particle approximation for the quasi-stationary distribution of a diffusion process: Uniform estimates in a compact soft case. ESAIM: PS 26 (2022) 1–25. [CrossRef] [EDP Sciences] [Google Scholar]
  32. L. Journel and P. Monmarché, Uniform convergence of the Fleming-Viot process in a hard killing metastable case. Preprint arXiv:2207.02030 (2022). [Google Scholar]
  33. O. Kallenberg, Foundations of Modern Probability, Probability and its Applications, 2nd edn. Springer-Verlag, New York (2002). [Google Scholar]
  34. T. Lelièvre, M. Rousset and G. Stoltz, Long-time convergence of an adaptive biasing force method. Nonlinearity 21 (2008) 1155–1181. [CrossRef] [MathSciNet] [Google Scholar]
  35. V. Lemaire, M. Thieullen and N. Thomas, Exact simulation of the jump times of a class of piecewise deterministic Markov processes. J. Sci. Comput. 75 (2018) 1776–1807. [CrossRef] [MathSciNet] [Google Scholar]
  36. P.A.W. Lewis and G.S. Shedler, Simulation of nonhomogeneous Poisson processes by thinning. Naval Res. Logist. Quart. 26 (1979) 403–413. [CrossRef] [MathSciNet] [Google Scholar]
  37. F. Malrieu, Logarithmic Sobolev inequalities for some nonlinear PDE’s. Stoch. Process. Appl. 95 (2001) 109–132. [CrossRef] [Google Scholar]
  38. J.C. Mattingly, Exponential convergence for the stochastically forced Navier-Stokes equations and other partially dissipative dynamics. Commun. Math. Phys. 230 (2002) 421–462. [CrossRef] [Google Scholar]
  39. J.C. Mattingly, On recent progress for the stochastic Navier Stokes equations, in Journées “Équations aux Dérivées Partielles”, Exp. No. XI, 52, Univ. Nantes, Nantes (2003). [Google Scholar]
  40. H.P. McKean, Jr., A class of Markov processes associated with nonlinear parabolic equations. Proc. Nat. Acad. Sci. U.S.A. 56 (1966) 1907–1911. [Google Scholar]
  41. S.P. Meyn and R.L. Tweedie, Stability of Markovian processes. III. Foster-Lyapunov criteria for continuous-time processes. Adv. Appl. Probab. 25 (1993) 518–548. [CrossRef] [MathSciNet] [Google Scholar]
  42. P. Monmarché, Weakly self-interacting piecewise deterministic bacterial chemotaxis. Markov Process. Related Fields 23 (2017) 609–659. [MathSciNet] [Google Scholar]
  43. P. Monmarché, Piecewise deterministic simulated annealing. ALEA Lat. Am. J. Probab. Math. Stat. 13 (2016) 357–398. [CrossRef] [MathSciNet] [Google Scholar]
  44. P. Monmarché, Long-time behaviour and propagation of chaos for mean field kinetic particles. Stoch. Process. Appl. 127 (2017) 1721–1737. [CrossRef] [Google Scholar]
  45. K. Pakdaman, B. Perthame and D. Salort, Dynamics of a structured neuron population. Nonlinearity 23 (2010) 55–75. [CrossRef] [MathSciNet] [Google Scholar]
  46. C.S. Patlak, Random walk with persistence and external bias. Bull. Math. Biophys. 15 (1953) 311–338. [Google Scholar]
  47. B. Perthame and D. Salort, On a voltage-conductance kinetic system for integrate & fire neural networks. Kinet. Relat. Models 6 (2013) 841–864. [CrossRef] [MathSciNet] [Google Scholar]
  48. F. Schlögl, Chemical reaction models for non-equilibrium phase transitions. Zeitschrift für Physik 253 (1972) 147–161. [CrossRef] [Google Scholar]
  49. R.H. Swendsen and J.-S. Wang, Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57 (1986) 2607–2609. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  50. A.-s. Sznitman, Topics in propagation of chaos, in École d’Été de Probabilités de Saint-Flour XIX—1989. Vol. 1464 of Lecture Notes in Math. Springer, Berlin (1991), pp. 165–251. [CrossRef] [Google Scholar]
  51. M.E. Thuckerman, B.J. Berne and A. Rossi, Moleculare dynamics algorithm for multiple time scales: Systems with disparate mass. J. Chem. Phys. 94 (1991) 1465–1469. [CrossRef] [Google Scholar]
  52. J. Tugaut, Phase transitions of McKean-Vlasov processes in double-wells landscape. Stochastics 86 (2014) 257–284. [CrossRef] [MathSciNet] [Google Scholar]
  53. J. Tugaut, Self-stabilizing processes in multi-wells landscape in d-invariant probabilities. J. Theoret. Probab. 27 (2014) 57–79. [CrossRef] [MathSciNet] [Google Scholar]
  54. P. Vanetti, A. Bouchard-Côté, G. Deligiannidis and A. Doucet, Piecewise deterministic markov processes for continuous-time Monte Carlo. Stat. Sci. 33 (2018) 386–412. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.