Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations

Anthony Le Cavil; Nadia Oudjane; Francesco Russo

doi:10.1080/17442508.2019.1594809

Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations

Anthony Le Cavil
, Nadia Oudjane
, Francesco Russo

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

Abstract

We propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.

Original language	English
Pages (from-to)	1206-1248
Number of pages	43
Journal	Stochastics
Volume	91
Issue number	8
DOIs	https://doi.org/10.1080/17442508.2019.1594809
Publication status	Published - 17 Nov 2019
Externally published	Yes

Keywords

35K58
60H10
60H30
60J60
65C05
65C35
Semilinear partial differential equations
nonlinear Feynman-Kac type functional
particle systems
probabilistic representation of PDEs

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10.1080/17442508.2019.1594809

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title = "Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations",

abstract = "We propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.",

keywords = "35K58, 60H10, 60H30, 60J60, 65C05, 65C35, Semilinear partial differential equations, nonlinear Feynman-Kac type functional, particle systems, probabilistic representation of PDEs",

author = "\{Le Cavil\}, Anthony and Nadia Oudjane and Francesco Russo",

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doi = "10.1080/17442508.2019.1594809",

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AU - Le Cavil, Anthony

AU - Oudjane, Nadia

AU - Russo, Francesco

PY - 2019/11/17

Y1 - 2019/11/17

N2 - We propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.

AB - We propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system.

KW - 35K58

KW - 60H10

KW - 60H30

KW - 60J60

KW - 65C05

KW - 65C35

KW - Semilinear partial differential equations

KW - nonlinear Feynman-Kac type functional

KW - particle systems

KW - probabilistic representation of PDEs

U2 - 10.1080/17442508.2019.1594809

DO - 10.1080/17442508.2019.1594809

M3 - Article

AN - SCOPUS:85063945798

SN - 1744-2508

VL - 91

SP - 1206

EP - 1248

JO - Stochastics

JF - Stochastics

IS - 8

ER -

Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations

Abstract

Keywords

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