Abstract
We present a general study relating the geometry of the graph 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 nondifferentiable stationary Gaussian process with local times will be Jarnik functions. This extends earlier works of Lifschitz and Pitt, which gave examples of Gaussian processes 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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