Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows

Gonçalo dos Reis; Vadim Platonov

doi:10.1007/s11118-022-10012-1

Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows

Gonçalo dos Reis, Vadim Platonov

CMA - Centro de Matemática e Aplicações

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

1 Citation (Scopus)

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Abstract

We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understood in the sense of Lions.

Original language	English
Journal	Potential Analysis
DOIs	https://doi.org/10.1007/s11118-022-10012-1
Publication status	Published - 31 May 2022

Keywords

Conditional measure flows
Full measure flows
Itô-Wentzell formula
Lions derivative
Stochastic differential equations

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10.1007/s11118-022-10012-1Licence: CC BY

Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure FlowsFinal published version, 628 KBLicence: CC BY

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title = "It{\^o}-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows",

abstract = "We present several It{\^o}-Wentzell formulae on Wiener spaces for real-valued functional random field of It{\^o} type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understood in the sense of Lions.",

keywords = "Conditional measure flows, Full measure flows, It{\^o}-Wentzell formula, Lions derivative, Stochastic differential equations",

author = "{dos Reis}, Gon{\c c}alo and Vadim Platonov",

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year = "2022",

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day = "31",

doi = "10.1007/s11118-022-10012-1",

language = "English",

journal = "Potential Analysis",

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AU - dos Reis, Gonçalo

AU - Platonov, Vadim

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PY - 2022/5/31

Y1 - 2022/5/31

N2 - We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understood in the sense of Lions.

AB - We present several Itô-Wentzell formulae on Wiener spaces for real-valued functional random field of Itô type that depend on measure flows. We distinguish the full- and the marginal-measure flow cases in the spirit of mean-field games. Derivatives with respect to the measure components are understood in the sense of Lions.

KW - Conditional measure flows

KW - Full measure flows

KW - Itô-Wentzell formula

KW - Lions derivative

KW - Stochastic differential equations

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U2 - 10.1007/s11118-022-10012-1

DO - 10.1007/s11118-022-10012-1

M3 - Article

AN - SCOPUS:85131093973

SN - 0926-2601

JO - Potential Analysis

JF - Potential Analysis

ER -

Itô-Wentzell-Lions Formula for Measure Dependent Random Fields under Full and Conditional Measure Flows

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