### Abstract

The motion of a particle acted on by the deterministic force vector b(x(t)) and perturbed by random forces of white noise type is considered. Such a particle will leave any bounded domain OMEGA in finite time. We consider the case where b is such tat the boundary consists of a trajectory or trajectories of the system dx/dt equals b(x(t)). Thus the cases of an unstable limit cycle and a center are considered. Expressions are derived for the mean first passage time to the boundary and the probability distribution of exit points on the boundary.

Original language | English (US) |
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Pages (from-to) | 822-834 |

Number of pages | 13 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 42 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 1982 |

### ASJC Scopus subject areas

- Applied Mathematics

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## Cite this

Matkowsky, B. J., & Schuss, Z. (1982). DIFFUSION ACROSS CHARACTERISTIC BOUNDARIES.

*SIAM Journal on Applied Mathematics*,*42*(4), 822-834. https://doi.org/10.1137/0142057