Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato’s class

Chongyang Ren; Xicheng Zhang

doi:10.3150/24-BEJ1775

Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato’s class

Chongyang Ren^*
, Xicheng Zhang

^*Corresponding author for this work

Wuhan University

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

1 Citation (Scopus)

Abstract

In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kato’s class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift b can be in the mixed L^qt^Lp1 x₁ L^p2 x₂ space with 2/q + d/p₁ + 3d/p₂ < 1. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in R^dN.

Original language	English
Pages (from-to)	1402-1427
Number of pages	26
Journal	Bernoulli
Volume	31
Issue number	2
DOIs	https://doi.org/10.3150/24-BEJ1775
Publication status	Published - May 2025
Externally published	Yes

Keywords

Heat kernel estimates
Kato’s class
Krylov’s estimate
kinetic SDEs

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10.3150/24-BEJ1775

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title = "Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato{\textquoteright}s class",

abstract = "In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with H{\"o}lder diffusion and unbounded singular drifts in Kato{\textquoteright}s class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift b can be in the mixed LqtLp1 x1 Lp2 x2 space with 2/q + d/p1 + 3d/p2 < 1. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in RdN.",

keywords = "Heat kernel estimates, Kato{\textquoteright}s class, Krylov{\textquoteright}s estimate, kinetic SDEs",

author = "Chongyang Ren and Xicheng Zhang",

year = "2025",

month = may,

doi = "10.3150/24-BEJ1775",

language = "English",

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pages = "1402--1427",

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T1 - Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato’s class

AU - Ren, Chongyang

AU - Zhang, Xicheng

PY - 2025/5

Y1 - 2025/5

N2 - In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kato’s class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift b can be in the mixed LqtLp1 x1 Lp2 x2 space with 2/q + d/p1 + 3d/p2 < 1. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in RdN.

AB - In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kato’s class. Moreover, we also establish sharp two-sided estimates for the density of the solution. In particular, the drift b can be in the mixed LqtLp1 x1 Lp2 x2 space with 2/q + d/p1 + 3d/p2 < 1. As an application, we show the existence and uniqueness of weak solution to a second order singular interacting particle system in RdN.

KW - Heat kernel estimates

KW - Kato’s class

KW - Krylov’s estimate

KW - kinetic SDEs

UR - https://www.scopus.com/pages/publications/85218725617

U2 - 10.3150/24-BEJ1775

DO - 10.3150/24-BEJ1775

M3 - Article

AN - SCOPUS:85218725617

SN - 1350-7265

VL - 31

SP - 1402

EP - 1427

JO - Bernoulli

JF - Bernoulli

IS - 2

ER -

Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato’s class

Abstract

Keywords

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