Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations

Zhongmin Qian; Panpan Ren; Feng-Yu Wang

doi:10.1137/24M1634473

Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations

Zhongmin Qian, Panpan Ren^*, Feng-Yu Wang

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

1 Citation (Scopus)

Abstract

The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy-cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker-Planck equations. Copyright © 2024 by SIAM.

Original language	English
Pages (from-to)	5330-5349
Journal	SIAM Journal on Mathematical Analysis
Volume	56
Issue number	4
Online published	19 Jul 2024
DOIs	https://doi.org/10.1137/24M1634473
Publication status	Published - Aug 2024

Research Keywords

degenerate diffusion process
entropy estimate
nonlinear kinetic Fokker-Planck equation
stochastic Hamiltonian system

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title = "Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations",

abstract = "The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy-cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker-Planck equations. Copyright {\textcopyright} 2024 by SIAM.",

keywords = "degenerate diffusion process, entropy estimate, nonlinear kinetic Fokker-Planck equation, stochastic Hamiltonian system",

author = "Zhongmin Qian and Panpan Ren and Feng-Yu Wang",

year = "2024",

month = aug,

doi = "10.1137/24M1634473",

language = "English",

volume = "56",

pages = "5330--5349",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics",

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TY - JOUR

T1 - Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations

AU - Qian, Zhongmin

AU - Ren, Panpan

AU - Wang, Feng-Yu

PY - 2024/8

Y1 - 2024/8

N2 - The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy-cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker-Planck equations. Copyright © 2024 by SIAM.

AB - The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy-cost inequality and exponential ergodicity in entropy are derived for distribution dependent stochastic Hamiltonian systems associated with nonlinear kinetic Fokker-Planck equations. Copyright © 2024 by SIAM.

KW - degenerate diffusion process

KW - entropy estimate

KW - nonlinear kinetic Fokker-Planck equation

KW - stochastic Hamiltonian system

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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85199526577&origin=recordpage

U2 - 10.1137/24M1634473

DO - 10.1137/24M1634473

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1410

VL - 56

SP - 5330

EP - 5349

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

Entropy Estimate for Degenerate SDEs with Applications to Nonlinear Kinetic Fokker–Planck Equations

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Research Keywords

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