This is a review paper about some problems of statistical inference for one-parameter stochastic processes, mainly based upon the observation of a convolution of the path with a non-random kernel. Most of the results are known and presented without proofs. The tools are first and second order approximation theorems of the occupation measure of the path, by means of functionals defined on the smoothed paths. Various classes of stochastic processes are considered starting with the Wiener process,...
We study the tails of the distribution of the maximum of a stationary gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [11] for a sufficiently small interval.
We study the tails of the distribution of the maximum of a stationary
Gaussian process on a bounded interval of the real line. Under regularity
conditions including the existence of the spectral moment of order ,
we give an additional term for this asymptotics. This widens the
application of an expansion given originally by Piterbarg [CITE] for
a sufficiently small interval.
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