Fokker–Planck equations with terminal condition and related McKean probabilistic representation

Lucas Izydorczyk; Nadia Oudjane; Francesco Russo; Gianmario Tessitore

doi:10.1007/s00030-021-00736-1

Fokker–Planck equations with terminal condition and related McKean probabilistic representation

Lucas Izydorczyk
, Nadia Oudjane
, Francesco Russo
, Gianmario Tessitore

Unité de Mathématiques Appliquées
Laboratoire de Finance des Marchés de l’énergie
Dipartimento di Matematica
University of Milano-Bicocca

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

3 Citations (Scopus)

Abstract

Usually Fokker–Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we give sufficient conditions for uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.

Original language	English
Article number	10
Journal	Nonlinear Differential Equations and Applications
Volume	29
Issue number	1
DOIs	https://doi.org/10.1007/s00030-021-00736-1
Publication status	Published - 1 Jan 2022

Keywords

Fokker Planck equation
Inverse problem
McKean stochastic differential equation
Probabilistic representation of PDEs
Time-reversed diffusion

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10.1007/s00030-021-00736-1

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title = "Fokker{\textendash}Planck equations with terminal condition and related McKean probabilistic representation",

abstract = "Usually Fokker{\textendash}Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we give sufficient conditions for uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.",

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author = "Lucas Izydorczyk and Nadia Oudjane and Francesco Russo and Gianmario Tessitore",

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AU - Izydorczyk, Lucas

AU - Oudjane, Nadia

AU - Russo, Francesco

AU - Tessitore, Gianmario

PY - 2022/1/1

Y1 - 2022/1/1

N2 - Usually Fokker–Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we give sufficient conditions for uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.

AB - Usually Fokker–Planck type partial differential equations (PDEs) are well-posed if the initial condition is specified. In this paper, alternatively, we consider the inverse problem which consists in prescribing final data: in particular we give sufficient conditions for uniqueness. In the second part of the paper we provide a probabilistic representation of those PDEs in the form of a solution of a McKean type equation corresponding to the time-reversal dynamics of a diffusion process.

KW - Fokker Planck equation

KW - Inverse problem

KW - McKean stochastic differential equation

KW - Probabilistic representation of PDEs

KW - Time-reversed diffusion

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DO - 10.1007/s00030-021-00736-1

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JO - Nonlinear Differential Equations and Applications

JF - Nonlinear Differential Equations and Applications

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M1 - 10

ER -

Fokker–Planck equations with terminal condition and related McKean probabilistic representation

Abstract

Keywords

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