Distribution dependent SDEs driven by additive continuous noise

Lucio Galeati; Fabian A. Harang; Avi Mayorcas

doi:10.1214/22-EJP756

Distribution dependent SDEs driven by additive continuous noise

Lucio Galeati, Fabian A. Harang, Avi Mayorcas

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (SciVal)

Abstract

We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.

Original language	English
Article number	37
Journal	Electronic Journal of Probability
Volume	27
DOIs	https://doi.org/10.1214/22-EJP756
Publication status	Published - 2022

Bibliographical note

Funding Information:
*FH gratefully acknowledges financial support from the STORM project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy – GZ 2047/1, project-id 390685813. †Institute of Applied Mathematics, University of Bonn, 53115 Endenicher Allee 60, Bonn, Germany ‡Department of Mathematics, University of Oslo, P.O. box 1053, Blindern, 0316, Oslo, Norway. E-mail: [email protected] §Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK. E-mail: [email protected]

Keywords

Additive noise
McKean–Vlasov equation
Mean field limit
Pathwise approach

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty

Access to Document

10.1214/22-EJP756Licence: CC BY

Cite this

@article{d9dd2130483e4ca386050f14ba86eca7,

title = "Distribution dependent SDEs driven by additive continuous noise",

abstract = "We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.",

keywords = "Additive noise, McKean–Vlasov equation, Mean field limit, Pathwise approach",

author = "Lucio Galeati and Harang, {Fabian A.} and Avi Mayorcas",

note = "Funding Information: *FH gratefully acknowledges financial support from the STORM project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany{\textquoteright}s Excellence Strategy – GZ 2047/1, project-id 390685813. †Institute of Applied Mathematics, University of Bonn, 53115 Endenicher Allee 60, Bonn, Germany ‡Department of Mathematics, University of Oslo, P.O. box 1053, Blindern, 0316, Oslo, Norway. E-mail: [email protected] §Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK. E-mail: [email protected]",

year = "2022",

doi = "10.1214/22-EJP756",

language = "English",

volume = "27",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Distribution dependent SDEs driven by additive continuous noise

AU - Galeati, Lucio

AU - Harang, Fabian A.

AU - Mayorcas, Avi

N1 - Funding Information: *FH gratefully acknowledges financial support from the STORM project 274410, funded by the Research Council of Norway. LG is funded by the DFG under Germany’s Excellence Strategy – GZ 2047/1, project-id 390685813. †Institute of Applied Mathematics, University of Bonn, 53115 Endenicher Allee 60, Bonn, Germany ‡Department of Mathematics, University of Oslo, P.O. box 1053, Blindern, 0316, Oslo, Norway. E-mail: [email protected] §Centre for Mathematical Sciences, Wilberforce Rd, Cambridge CB3 0WA, UK. E-mail: [email protected]

PY - 2022

Y1 - 2022

N2 - We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.

AB - We study distribution dependent stochastic differential equation driven by a continuous process, without any specification on its law, following the approach initiated in [17]. We provide several criteria for existence and uniqueness of solutions which go beyond the classical globally Lipschitz setting. In particular we show well-posedness of the equation, as well as almost sure convergence of the associated particle system, for drifts satisfying either Osgood-continuity, monotonicity, local Lipschitz or Sobolev differentiability type assumptions.

KW - Additive noise

KW - McKean–Vlasov equation

KW - Mean field limit

KW - Pathwise approach

UR - http://www.scopus.com/inward/record.url?scp=85126288920&partnerID=8YFLogxK

U2 - 10.1214/22-EJP756

DO - 10.1214/22-EJP756

M3 - Article

AN - SCOPUS:85126288920

SN - 1083-6489

VL - 27

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 37

ER -

Distribution dependent SDEs driven by additive continuous noise

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this