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Using a probabilistic method for number theoretic purposes, I have encountered the following question (it may be very standard):

Let $X_t$ be a Gaussian process $(t>0)$ such that $X_0=0$. What is the expected number of times for the process to cross zero in the interval $[0,c)$ as a function of $c$?

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up vote 4 down vote accepted

The magic words are "Kac-Rice formula". This is exactly the question which comes up in analyzing zeros of random polynomials.

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Thank you! It was most helpful. – TOM Jul 25 '13 at 1:38

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