A stochastic representation for the level set equations

H. Mete Soner; Nizar Touzi

doi:10.1081/PDE-120016135

A stochastic representation for the level set equations

H. Mete Soner, Nizar Touzi

Finance and Risk Engineering

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

Abstract

A Feynman-Kac representation is proved for geometric partial differential equations. This representation is in terms of a stochastic target problem. In this problem the controller tries to steer a controlled process into a given target by judicial choices of controls. The sublevel sets of the unique level set solution of the geometric equation is shown to coincide with the reachability sets of the target problem whose target is the sublevel set of the final data.

Original language	English (US)
Pages (from-to)	2031-2053
Number of pages	23
Journal	Communications in Partial Differential Equations
Volume	27
Issue number	9-10
DOIs	https://doi.org/10.1081/PDE-120016135
State	Published - 2002

Keywords

Codimension k mean curvature flow
Geometric flows
Inverse mean curvature flow
Stochastic target problem

ASJC Scopus subject areas

Analysis
Applied Mathematics

Access to Document

10.1081/PDE-120016135

Cite this

@article{a0f533470c5d457abd660f131235499d,

title = "A stochastic representation for the level set equations",

abstract = "A Feynman-Kac representation is proved for geometric partial differential equations. This representation is in terms of a stochastic target problem. In this problem the controller tries to steer a controlled process into a given target by judicial choices of controls. The sublevel sets of the unique level set solution of the geometric equation is shown to coincide with the reachability sets of the target problem whose target is the sublevel set of the final data.",

keywords = "Codimension k mean curvature flow, Geometric flows, Inverse mean curvature flow, Stochastic target problem",

author = "Soner, {H. Mete} and Nizar Touzi",

year = "2002",

doi = "10.1081/PDE-120016135",

language = "English (US)",

volume = "27",

pages = "2031--2053",

journal = "Communications in Partial Differential Equations",

issn = "0360-5302",

publisher = "Taylor and Francis Ltd.",

number = "9-10",

}

TY - JOUR

T1 - A stochastic representation for the level set equations

AU - Soner, H. Mete

AU - Touzi, Nizar

PY - 2002

Y1 - 2002

N2 - A Feynman-Kac representation is proved for geometric partial differential equations. This representation is in terms of a stochastic target problem. In this problem the controller tries to steer a controlled process into a given target by judicial choices of controls. The sublevel sets of the unique level set solution of the geometric equation is shown to coincide with the reachability sets of the target problem whose target is the sublevel set of the final data.

AB - A Feynman-Kac representation is proved for geometric partial differential equations. This representation is in terms of a stochastic target problem. In this problem the controller tries to steer a controlled process into a given target by judicial choices of controls. The sublevel sets of the unique level set solution of the geometric equation is shown to coincide with the reachability sets of the target problem whose target is the sublevel set of the final data.

KW - Codimension k mean curvature flow

KW - Geometric flows

KW - Inverse mean curvature flow

KW - Stochastic target problem

UR - http://www.scopus.com/inward/record.url?scp=0036908999&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036908999&partnerID=8YFLogxK

U2 - 10.1081/PDE-120016135

DO - 10.1081/PDE-120016135

M3 - Article

AN - SCOPUS:0036908999

SN - 0360-5302

VL - 27

SP - 2031

EP - 2053

JO - Communications in Partial Differential Equations

JF - Communications in Partial Differential Equations

IS - 9-10

ER -

A stochastic representation for the level set equations

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this