A stochastic representation for the level set equations

H. Mete Soner, Nizar Touzi

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

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 languageEnglish (US)
Pages (from-to)2031-2053
Number of pages23
JournalCommunications in Partial Differential Equations
Volume27
Issue number9-10
DOIs
StatePublished - Dec 1 2002
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Keywords

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

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