Accession Number:

ADA218337

Title:

On the Existence of Local Times: A Geometric Study

Descriptive Note:

Technical rept.

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES

Report Date:

1990-01-01

Pagination or Media Count:

63.0

Abstract:

We present a general study relating the geometry of the graphs of a real function to the existence of local times for the function. The general results obtained are applied to Gaussian processes, and we show that with probability 1 the sample functions of a non-differentiable stationary Gaussian process with local times will be Jarnik functions. This extends earlier works of Lifshitz and Pitt, which gave examples of Gaussian process without local times. An example is given of a Jarnik function without local times thus answering negatively a question raised by Geman and Horowitz.

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE