Euler scheme for density dependent stochastic differential equations

Zimo Hao; Michael Röckner; Xicheng Zhang

doi:10.1016/j.jde.2020.11.018

Euler scheme for density dependent stochastic differential equations

Zimo Hao, Michael Röckner, Xicheng Zhang^*

^*Corresponding author for this work

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

7 Citations (Scopus)

Abstract

In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the associated nonlinear Fokker-Planck equation. As an application, we obtain the well-posedness of a nonlinear Fokker-Planck equation.

Original language	English
Pages (from-to)	996-1014
Number of pages	19
Journal	Journal of Differential Equations
Volume	274
DOIs	https://doi.org/10.1016/j.jde.2020.11.018
Publication status	Published - 15 Feb 2021
Externally published	Yes

Keywords

Density dependent SDE
Heat kernel
Strong solution

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10.1016/j.jde.2020.11.018

Cite this

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title = "Euler scheme for density dependent stochastic differential equations",

abstract = "In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the associated nonlinear Fokker-Planck equation. As an application, we obtain the well-posedness of a nonlinear Fokker-Planck equation.",

keywords = "Density dependent SDE, Heat kernel, Strong solution",

author = "Zimo Hao and Michael R{\"o}ckner and Xicheng Zhang",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = feb,

day = "15",

doi = "10.1016/j.jde.2020.11.018",

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T1 - Euler scheme for density dependent stochastic differential equations

AU - Hao, Zimo

AU - Röckner, Michael

AU - Zhang, Xicheng

PY - 2021/2/15

Y1 - 2021/2/15

N2 - In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the associated nonlinear Fokker-Planck equation. As an application, we obtain the well-posedness of a nonlinear Fokker-Planck equation.

AB - In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation for density dependent SDEs and the uniqueness is based on the associated nonlinear Fokker-Planck equation. As an application, we obtain the well-posedness of a nonlinear Fokker-Planck equation.

KW - Density dependent SDE

KW - Heat kernel

KW - Strong solution

UR - http://www.scopus.com/inward/record.url?scp=85096405309&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2020.11.018

DO - 10.1016/j.jde.2020.11.018

M3 - Article

AN - SCOPUS:85096405309

SN - 0022-0396

VL - 274

SP - 996

EP - 1014

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Euler scheme for density dependent stochastic differential equations

Abstract

Keywords

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