McKean-Vlasov SPDEs with Additive Noise as Limits of Weighted Interacting Particle Systems

Letizia Angeli; Martin Kolodziejczyk; Michela Ottobre

doi:10.1007/978-3-031-57005-6_2

McKean-Vlasov SPDEs with Additive Noise as Limits of Weighted Interacting Particle Systems

Letizia Angeli, Martin Kolodziejczyk, Michela Ottobre^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper we consider McKean-Vlasov Partial Differential Equations (PDEs) perturbed by additive (infinite dimensional) noise. The resulting dynamics is a McKean-Vlasov SPDE or, more precisely, the Stochastic McKean-Vlasov (SMKV) equation with additive noise. It is well known that McKean-Vlasov PDEs and SMKV equations with multiplicative (gradient) noise can be obtained as limits of empirical measures of appropriate interacting particle systems. However, it is unclear whether and how one can construct interacting particle systems which converge to SMKV PDEs with additive noise. This is the question we aim to answer in this brief article.

Original language	English
Title of host publication	Women in Analysis and PDE
Publisher	Springer
Pages	7-16
Number of pages	10
ISBN (Electronic)	9783031570056
ISBN (Print)	9783031570049
DOIs	https://doi.org/10.1007/978-3-031-57005-6_2
Publication status	Published - 17 Oct 2024

Publication series

Name	Trends in Mathematics
Volume	5
ISSN (Print)	2297-0215
ISSN (Electronic)	2297-024X

Keywords

Interacting particle systems
Particle approximations to stochastic partial differential equations
Stochastic McKean-Vlasov equation
Stochastic partial differential equations

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/978-3-031-57005-6_2

Cite this

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title = "McKean-Vlasov SPDEs with Additive Noise as Limits of Weighted Interacting Particle Systems",

abstract = "In this paper we consider McKean-Vlasov Partial Differential Equations (PDEs) perturbed by additive (infinite dimensional) noise. The resulting dynamics is a McKean-Vlasov SPDE or, more precisely, the Stochastic McKean-Vlasov (SMKV) equation with additive noise. It is well known that McKean-Vlasov PDEs and SMKV equations with multiplicative (gradient) noise can be obtained as limits of empirical measures of appropriate interacting particle systems. However, it is unclear whether and how one can construct interacting particle systems which converge to SMKV PDEs with additive noise. This is the question we aim to answer in this brief article.",

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author = "Letizia Angeli and Martin Kolodziejczyk and Michela Ottobre",

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AU - Angeli, Letizia

AU - Kolodziejczyk, Martin

AU - Ottobre, Michela

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

PY - 2024/10/17

Y1 - 2024/10/17

N2 - In this paper we consider McKean-Vlasov Partial Differential Equations (PDEs) perturbed by additive (infinite dimensional) noise. The resulting dynamics is a McKean-Vlasov SPDE or, more precisely, the Stochastic McKean-Vlasov (SMKV) equation with additive noise. It is well known that McKean-Vlasov PDEs and SMKV equations with multiplicative (gradient) noise can be obtained as limits of empirical measures of appropriate interacting particle systems. However, it is unclear whether and how one can construct interacting particle systems which converge to SMKV PDEs with additive noise. This is the question we aim to answer in this brief article.

AB - In this paper we consider McKean-Vlasov Partial Differential Equations (PDEs) perturbed by additive (infinite dimensional) noise. The resulting dynamics is a McKean-Vlasov SPDE or, more precisely, the Stochastic McKean-Vlasov (SMKV) equation with additive noise. It is well known that McKean-Vlasov PDEs and SMKV equations with multiplicative (gradient) noise can be obtained as limits of empirical measures of appropriate interacting particle systems. However, it is unclear whether and how one can construct interacting particle systems which converge to SMKV PDEs with additive noise. This is the question we aim to answer in this brief article.

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KW - Particle approximations to stochastic partial differential equations

KW - Stochastic McKean-Vlasov equation

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McKean-Vlasov SPDEs with Additive Noise as Limits of Weighted Interacting Particle Systems

Abstract

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