Bernoulli

  • Bernoulli
  • Volume 5, Number 6 (1999), 1035-1058.

Some asymptotic properties of the local time of the uniform empirical process

Miklós Csörgö, Zhan Shi, and Marc Yor

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Abstract

We study the almost sure asymptotic properties of the local time of the uniform empirical process. In particular, we obtain two versions of the law of the iterated logarithm for the integral of the square of the local time. It is interesting to note that the corresponding problems for the Wiener process remain open. Properties of Lp-norms of the local time are studied. We also characterize the joint asymptotics of the local time at a fixed level and the maximum local time.

Article information

Source
Bernoulli, Volume 5, Number 6 (1999), 1035-1058.

Dates
First available in Project Euclid: 23 March 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1143122302

Mathematical Reviews number (MathSciNet)
MR1735784

Zentralblatt MATH identifier
0960.60023

Keywords
Brownian bridge empirical process local time

Citation

Csörgö, Miklós; Shi, Zhan; Yor, Marc. Some asymptotic properties of the local time of the uniform empirical process. Bernoulli 5 (1999), no. 6, 1035--1058. https://projecteuclid.org/euclid.bj/1143122302


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