Constrained overdamped Langevin dynamics for symmetric multimarginal optimal transportation

Autor: Aurélien Alfonsi, Rafaël Coyaud, Virginie Ehrlacher

Publikováno v: Mathematical Models and Methods in Applied Sciences
Mathematical Models and Methods in Applied Sciences, World Scientific Publishing, In press
Mathematical Models and Methods in Applied Sciences, In press

The Strictly Correlated Electrons (SCE) limit of the Levy–Lieb functional in Density Functional Theory (DFT) gives rise to a symmetric multi-marginal optimal transport problem with Coulomb cost, where the number of marginal laws is equal to the num

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3ef1765da109929bf98d4619c3f493a3
https://hal.archives-ouvertes.fr/hal-03131763/document

A generic construction for high order approximation schemes of semigroups using random grids

Autor: Aurélien Alfonsi, Vlad Bally

Publikováno v: Numerische Mathematik
Numerische Mathematik, 2021, ⟨10.1007/s00211-021-01219-2⟩
Numerische Mathematik, Springer Verlag, 2021, ⟨10.1007/s00211-021-01219-2⟩

Our aim is to construct high order approximation schemes for general semigroups of linear operators $$P_{t},t\ge 0$$ . In order to do it, we fix a time horizon T and the discretization steps $$h_{l}=\frac{T}{n^{l}},l\in {\mathbb {N}}$$ and we suppose

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https://hal-enpc.archives-ouvertes.fr/hal-02406433

Squared quadratic Wasserstein distance: optimal couplings and Lions differentiability

Autor: Benjamin Jourdain, Aurélien Alfonsi

Publikováno v: ESAIM: Probability and Statistics
ESAIM: Probability and Statistics, EDP Sciences, 2020, 24, pp.703-717. ⟨10.1051/ps/2020013⟩
ESAIM: Probability and Statistics, 2020, 24, pp.703-717. ⟨10.1051/ps/2020013⟩

In this paper, we remark that any optimal coupling for the quadratic Wasserstein distanceW22(μ,ν) between two probability measuresμandνwith finite second order moments on ℝdis the composition of a martingale coupling with an optimal transport m

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https://hal.archives-ouvertes.fr/hal-01934705

Sampling of one-dimensional probability measures in the convex order and computation of robust option price bounds

Autor: Jacopo Corbetta, Benjamin Jourdain, Aurélien Alfonsi

Publikováno v: International Journal of Theoretical and Applied Finance
International Journal of Theoretical and Applied Finance, World Scientific Publishing, 2019, 22 (3), ⟨10.1142/S021902491950002X⟩
International Journal of Theoretical and Applied Finance, 2019, 22 (3), ⟨10.1142/S021902491950002X⟩

For [Formula: see text] and [Formula: see text] two probability measures on the real line such that [Formula: see text] is smaller than [Formula: see text] in the convex order, this property is in general not preserved at the level of the empirical m

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::40a3f91b94caf5fee77606d287536ac5
https://hal-enpc.archives-ouvertes.fr/hal-01963507/file/simu_cvx_order_1D_v2.pdf

Parametrix Methods for One-Dimensional Reflected SDEs

Autor: Masafumi Hayashi, Aurélien Alfonsi, Arturo Kohatsu-Higa

Publikováno v: Modern Problems of Stochastic Analysis and StatisticsSelected Contributions In Honor of Valentin Konakov
Modern Problems of Stochastic Analysis and Statistics Selected Contributions In Honor of Valentin Konakov, Springer Proceedings in Mathematics & Statistics (208), Springer, 2017, 978-3-319-65313-6. ⟨10.1007/978-3-319-65313-6_3⟩
Springer Proceedings in Mathematics & Statistics ISBN: 9783319653129

International audience; In this article, we revisit in a didactic manner the forward and backward approaches of the parametrix method for one-dimensional reflected stochastic differential equations on the half line. We give probabilistic expressions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0b8afd88533d2fe3f9cb9721bce54eb4
https://hal-enpc.archives-ouvertes.fr/hal-01670011