### 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) |
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Pages (from-to) | 2031-2053 |

Number of pages | 23 |

Journal | Communications in Partial Differential Equations |

Volume | 27 |

Issue number | 9-10 |

DOIs | |

State | Published - Dec 1 2002 |

Externally published | Yes |

### 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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## Cite this

Soner, H. M., & Touzi, N. (2002). A stochastic representation for the level set equations.

*Communications in Partial Differential Equations*,*27*(9-10), 2031-2053. https://doi.org/10.1081/PDE-120016135