Bismut formula for Lions derivative of distribution-path dependent SDEs

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

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Author(s)

Detail(s)

Original languageEnglish
Pages (from-to)285-329
Journal / PublicationJournal of Differential Equations
Volume282
Online published19 Feb 2021
Publication statusPublished - 5 May 2021
Externally publishedYes

Link(s)

DOI

DOI
Check@CityULib
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-85101178152&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(e758a5dc-cd61-43fd-beb8-9b38d598fa50).html

Abstract

To characterize the regularity of distribution-path dependent SDEs in the initial distribution which varies as probability measure on the path space, we introduce the intrinsic and Lions derivatives for probability measures on Banach spaces, and prove the chain rule of the Lions derivative for the distribution of Banach-valued random variables. By using Malliavin calculus, we establish the Bismut type formula for the Lions derivatives of functional solutions to SDEs with distribution-path dependent drifts. When the noise term is also path dependent so that the Bismut formula is invalid, we establish the asymptotic Bismut formula. Both non-degenerate and degenerate noises are considered. The main results of this paper generalize and improve the corresponding ones derived recently in the literature for the classical SDEs with memory and McKean-Vlasov SDEs without memory.

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Research Area(s)

  • Asymptotic Bismut formula, Bismut formula, Distribution-path dependent SDEs, Lions derivative, Malliavin calculus

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Publication fingerprints text

100
Path-dependent SDEs Keyphrases
100
Bismut Formula Keyphrases
100
Lions Derivative Keyphrases
100
Distribution Path Keyphrases
100
distribution INIS
100
Derivatives Mathematics
50
Probability Measure Keyphrases
50
Path Dependence Keyphrases
40
probability INIS
40
noise INIS
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Citation Format(s)

[ RIS ] [ BibTeX ]
Bismut formula for Lions derivative of distribution-path dependent SDEs. / Bao, Jianhai; Ren, Panpan; Wang, Feng-Yu.
In: Journal of Differential Equations, Vol. 282, 05.05.2021, p. 285-329.

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