### 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 |
---|---|

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 |

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### Keywords

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

### Cite this

*Probability Theory and Related Fields*,

*99*(3), 389-397. https://doi.org/10.1007/BF01199898

}

*Probability Theory and Related Fields*, vol. 99, no. 3, pp. 389-397. https://doi.org/10.1007/BF01199898

**Asymptotics of the generating function for the volume of the Wiener sausage.** / van den Berg, Michiel; Bolthausen, Erwin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Asymptotics of the generating function for the volume of the Wiener sausage

AU - van den Berg, Michiel

AU - Bolthausen, Erwin

PY - 1994/9

Y1 - 1994/9

N2 - 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.

AB - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=21344478871&partnerID=8YFLogxK

U2 - 10.1007/BF01199898

DO - 10.1007/BF01199898

M3 - Article

VL - 99

SP - 389

EP - 397

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 3

ER -