Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean

Autor: Benjamin Jourdain, Oumaima Bencheikh

Publikováno v: ESAIM: Proceedings and Surveys, Vol 65, Pp 219-235 (2019)
ESAIM: Proceedings and Surveys
ESAIM: Proceedings and Surveys, 2019, CEMRACS 2017-Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.219-235. ⟨10.1051/proc/201965219⟩
ESAIM: Proceedings and Surveys, EDP Sciences, 2019, CEMRACS 2017-Numerical methods for stochastic models: control, uncertainty quantification, mean-field, 65, pp.219-235. ⟨10.1051/proc/201965219⟩

In this paper, we prove that the weak error between a stochastic differential equation with nonlinearity in the sense of McKean given by moments and its approximation by the Euler discretization with time-step h of a system of N interacting particles

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::28fad2aff8a0c9d4ce6684964c95a8c2
https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196509.pdf

A new family of one dimensional martingale couplings

Autor: Benjamin Jourdain, William Margheriti

Publikováno v: Electron. J. Probab.
Electronic Journal of Probability
Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2020, 25 (136), pp.1-50. ⟨10.1214/20-EJP543⟩
Electronic Journal of Probability, 2020, 25 (136), pp.1-50. ⟨10.1214/20-EJP543⟩

In this paper, we exhibit a new family of martingale couplings between two one-dimensional probability measures $\mu $ and $\nu $ in the convex order. This family is parametrised by two dimensional probability measures on the unit square with respect

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23c6e7efb511095471795bfbfc072942
https://doi.org/10.1214/20-ejp543

Optimal dual quantizers of 1D log-concave distributions: Uniqueness and Lloyd like algorithm

Autor: Benjamin Jourdain, Gilles Pagès

Publikováno v: Journal of Approximation Theory. 267:105581

We establish for dual quantization the counterpart of Kieffer’s uniqueness result for compactly supported one dimensional probability distributions having a log -concave density (also called strongly unimodal): for such distributions, L r -optimal

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::573cbfd72995ede4bda933cf6f29be89
https://doi.org/10.1016/j.jat.2021.105581

Ninomiya-Victoir scheme : Multilevel Monte Carlo estimators and discretization of the involved Ordinary Differential Equations

Autor: Emmanuelle Clément, Anis Al Gerbi, Benjamin Jourdain

Publikováno v: ESAIM: Proceedings and Surveys
ESAIM: Proceedings and Surveys, EDP Sciences, 2017, 59, pp.1-14. ⟨10.1051/proc/201759001⟩
ESAIM: Proceedings and Surveys, Vol 59, Pp 1-14 (2017)

International audience; In this paper, we recall the result about the strong convergence rate of the Ninomiya-Victoir scheme and the properties of the multilevel Monte Carlo estimators involving this scheme that we introduced and studied in [2]. We a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6740cb5112040e3344345c270a998b4f
https://doi.org/10.1051/proc/201759001

Convex order, quantization and monotone approximations of ARCH models

Autor: Gilles PAGÈS, Benjamin Jourdain

Publikováno v: Journal of Theoretical Probability
Journal of Theoretical Probability, 2022, 35 (4), pp.2480-2517. ⟨10.1007/s10959-021-01141-1⟩
Journal of Theoretical Probability, Springer, 2022, 35 (4), pp.2480-2517. ⟨10.1007/s10959-021-01141-1⟩

International audience; We are interested in proposing approximations of a sequence of probability measures in the convex order by finitely supported probability measures still in the convex order. We propose to alternate transitions according to a m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b3cffa1a04387706fe46e81b5734e242
https://hal.archives-ouvertes.fr/hal-02304190