### Abstract

We consider the generating function {Mathematical expression} of the voltime of the Wiener sausage C_{?}(t), which is the e-neighbourhood of the Wiener path in the time interval [0, t]. For ?<0, the limiting behavior for t?8, up to logarithmic equivalence, had been determined in a celebrated work of Donsker and Varadhan. For ?>0 it had been investigated by van den Berg and Tóth, but in contrast to the case ?<0, there is no simple expression for the exponential rate known. We determine the asymptotic behaviour of this rate for small and large ?. © 1984 Springer-Verlag.

Original language | English |
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Pages (from-to) | 389-397 |

Number of pages | 9 |

Journal | Probability Theory and Related Fields |

Volume | 99 |

Issue number | 3 |

DOIs | |

Publication status | Published - Sep 1994 |

### Keywords

- Mathematics Subject Classification (1994): 60J65, 60F10, 60J45

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## Cite this

van den Berg, M., & Bolthausen, E. (1994). Asymptotics of the generating function for the volume of the Wiener sausage.

*Probability Theory and Related Fields*,*99*(3), 389-397. https://doi.org/10.1007/BF01199898