On the Existence of Local Times: A Geometric Study

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1990
Accession Number
ADA218337

Entities

People

  • J. M. Anderson
  • Joseph Horowitz
  • L. D. Pitt

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Data Science
  • Distribution Functions
  • Gaussian Processes
  • Information Science
  • Measure Theory
  • North Carolina
  • Probability
  • Random Variables
  • Random Walk
  • Sequences
  • Stationary
  • Stationary Processes
  • Statistics
  • Stochastic Processes
  • Theorems
  • Two Dimensional
  • Universities

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Military History
  • Statistical inference.