On the Existence of Local Times: A Geometric Study
NORTH CAROLINA UNIV AT CHAPEL HILL CENTER FOR STOCHASTIC PROCESSES
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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.
- Statistics and Probability