A discretized version of krylov’s estimate and its applications*

Xicheng Zhang

doi:10.1214/19-EJP390

A discretized version of krylov’s estimate and its applications^*

Xicheng Zhang^*

^*Corresponding author for this work

Wuhan University

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

21 Citations (Scopus)

Abstract

In this paper we prove a discretized version of Krylov’s estimate for discretized Itô processes. As applications, we study the weak and strong convergences for Euler’s approximation of mean-field SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler’s approximation of mean-field SDEs.

Original language	English
Article number	131
Journal	Electronic Journal of Probability
Volume	24
DOIs	https://doi.org/10.1214/19-EJP390
Publication status	Published - 2019
Externally published	Yes

Keywords

Euler’s scheme
Krylov’s estimate
Mean-field SDE
Propagation of chaos

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10.1214/19-EJP390

Cite this

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title = "A discretized version of krylov{\textquoteright}s estimate and its applications* ",

abstract = "In this paper we prove a discretized version of Krylov{\textquoteright}s estimate for discretized It{\^o} processes. As applications, we study the weak and strong convergences for Euler{\textquoteright}s approximation of mean-field SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler{\textquoteright}s approximation of mean-field SDEs.",

keywords = "Euler{\textquoteright}s scheme, Krylov{\textquoteright}s estimate, Mean-field SDE, Propagation of chaos",

author = "Xicheng Zhang",

year = "2019",

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language = "English",

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journal = "Electronic Journal of Probability",

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AU - Zhang, Xicheng

PY - 2019

Y1 - 2019

N2 - In this paper we prove a discretized version of Krylov’s estimate for discretized Itô processes. As applications, we study the weak and strong convergences for Euler’s approximation of mean-field SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler’s approximation of mean-field SDEs.

AB - In this paper we prove a discretized version of Krylov’s estimate for discretized Itô processes. As applications, we study the weak and strong convergences for Euler’s approximation of mean-field SDEs with measurable discontinuous and linear growth coefficients. Moreover, we also show the propagation of chaos for Euler’s approximation of mean-field SDEs.

KW - Euler’s scheme

KW - Krylov’s estimate

KW - Mean-field SDE

KW - Propagation of chaos

UR - https://www.scopus.com/pages/publications/85075051637

U2 - 10.1214/19-EJP390

DO - 10.1214/19-EJP390

M3 - Article

AN - SCOPUS:85075051637

SN - 1083-6489

VL - 24

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 131

ER -

A discretized version of krylov’s estimate and its applications^*

Abstract

Keywords

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