McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations

Lucas Izydorczyk; Nadia Oudjane; Francesco Russo

doi:10.1007/978-3-030-87432-2_10

McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations

Lucas Izydorczyk
, Nadia Oudjane
, Francesco Russo

Unité de Mathématiques Appliquées
EDF R&D
Laboratoire de Finance des Marchés de l’énergie

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control. MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.

langue originale	Anglais
titre	Geometry and Invariance in Stochastic Dynamics
rédacteurs en chef	Stefania Ugolini, Marco Fuhrman, Elisa Mastrogiacomo, Paola Morando, Barbara Rüdiger
Editeur	Springer
Pages	187-212
Nombre de pages	26
ISBN (imprimé)	9783030874315
Les DOIs	https://doi.org/10.1007/978-3-030-87432-2_10
état	Publié - 1 janv. 2021
Evénement	International Conference on Random Transformations and Invariance in Stochastic Dynamics, RTISD 2019 - Verona, Italie Durée: 25 mars 2019 → 29 mars 2019

Série de publications

Nom	Springer Proceedings in Mathematics and Statistics
Volume	378
ISSN (imprimé)	2194-1009
ISSN (Electronique)	2194-1017

Une conférence

Une conférence	International Conference on Random Transformations and Invariance in Stochastic Dynamics, RTISD 2019
Pays/Territoire	Italie
La ville	Verona
période	25/03/19 → 29/03/19

Accès au document

10.1007/978-3-030-87432-2_10

Contient cette citation

Izydorczyk, L., Oudjane, N., & Russo, F. (2021). McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations. Dans S. Ugolini, M. Fuhrman, E. Mastrogiacomo, P. Morando, & B. Rüdiger (eds.), Geometry and Invariance in Stochastic Dynamics (p. 187-212). (Springer Proceedings in Mathematics and Statistics; Vol 378). Springer. https://doi.org/10.1007/978-3-030-87432-2_10

Izydorczyk, Lucas ; Oudjane, Nadia ; Russo, Francesco. / McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations. Geometry and Invariance in Stochastic Dynamics. Editeur / Stefania Ugolini ; Marco Fuhrman ; Elisa Mastrogiacomo ; Paola Morando ; Barbara Rüdiger. Springer, 2021. p. 187-212 (Springer Proceedings in Mathematics and Statistics).

@inproceedings{1bd981f28a8d44429aa23014f40f63bc,

title = "McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations",

abstract = "This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control. MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.",

keywords = "Backward diffusion, Feynman-Kac measures, HJB equation, McKean stochastic differential equation, Probabilistic representation of PDEs, Time reversed diffusion",

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

note = "Publisher Copyright: {\textcopyright} 2021, Springer Nature Switzerland AG.; International Conference on Random Transformations and Invariance in Stochastic Dynamics, RTISD 2019 ; Conference date: 25-03-2019 Through 29-03-2019",

year = "2021",

month = jan,

day = "1",

doi = "10.1007/978-3-030-87432-2\_10",

language = "English",

isbn = "9783030874315",

series = "Springer Proceedings in Mathematics and Statistics",

publisher = "Springer",

pages = "187--212",

editor = "Stefania Ugolini and Marco Fuhrman and Elisa Mastrogiacomo and Paola Morando and Barbara R{\"u}diger",

booktitle = "Geometry and Invariance in Stochastic Dynamics",

}

Izydorczyk, L, Oudjane, N & Russo, F 2021, McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations. Dans S Ugolini, M Fuhrman, E Mastrogiacomo, P Morando & B Rüdiger (eds), Geometry and Invariance in Stochastic Dynamics. Springer Proceedings in Mathematics and Statistics, VOL. 378, Springer, p. 187-212, International Conference on Random Transformations and Invariance in Stochastic Dynamics, RTISD 2019, Verona, Italie, 25/03/19. https://doi.org/10.1007/978-3-030-87432-2_10

McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations. / Izydorczyk, Lucas; Oudjane, Nadia; Russo, Francesco.
Geometry and Invariance in Stochastic Dynamics. Ed. / Stefania Ugolini; Marco Fuhrman; Elisa Mastrogiacomo; Paola Morando; Barbara Rüdiger. Springer, 2021. p. 187-212 (Springer Proceedings in Mathematics and Statistics; Vol 378).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

TY - GEN

T1 - McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations

AU - Izydorczyk, Lucas

AU - Oudjane, Nadia

AU - Russo, Francesco

PY - 2021/1/1

Y1 - 2021/1/1

N2 - This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control. MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.

AB - This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control. MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.

KW - Backward diffusion

KW - Feynman-Kac measures

KW - HJB equation

KW - McKean stochastic differential equation

KW - Probabilistic representation of PDEs

KW - Time reversed diffusion

U2 - 10.1007/978-3-030-87432-2_10

DO - 10.1007/978-3-030-87432-2_10

M3 - Conference contribution

AN - SCOPUS:85125246544

SN - 9783030874315

T3 - Springer Proceedings in Mathematics and Statistics

SP - 187

EP - 212

BT - Geometry and Invariance in Stochastic Dynamics

A2 - Ugolini, Stefania

A2 - Fuhrman, Marco

A2 - Mastrogiacomo, Elisa

A2 - Morando, Paola

A2 - Rüdiger, Barbara

PB - Springer

T2 - International Conference on Random Transformations and Invariance in Stochastic Dynamics, RTISD 2019

Y2 - 25 March 2019 through 29 March 2019

ER -

Izydorczyk L, Oudjane N, Russo F. McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations. Dans Ugolini S, Fuhrman M, Mastrogiacomo E, Morando P, Rüdiger B, rédacteurs en chef, Geometry and Invariance in Stochastic Dynamics. Springer. 2021. p. 187-212. (Springer Proceedings in Mathematics and Statistics). doi: 10.1007/978-3-030-87432-2_10

McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations

Résumé

Série de publications

Une conférence

Accès au document

Empreinte digitale

Contient cette citation