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Smoothing and occupation measures of stochastic processes. (English) Zbl 1121.62072

Summary: 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, Gaussian processes, continuous semi-martingales and Lévy processes. Some statistical applications are also included in the text.

MSC:

62M02 Markov processes: hypothesis testing
60G48 Generalizations of martingales
60J60 Diffusion processes
62M09 Non-Markovian processes: estimation
60G15 Gaussian processes
60G51 Processes with independent increments; Lévy processes
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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References:

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