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Quadratic variations along irregular subdivisions for Gaussian processes. (English) Zbl 1109.60024

Summary: We deal with second order quadratic variations along general subdivisions for processes with Gaussian increments. These have almost surely a deterministic limit under conditions on the mesh of the subdivisions. This limit depends on the singularity function of the process and on the structure of the subdivisions, too. Then we illustrate the results with the example of the time-space deformed fractional Brownian motion and we present some simulations.

MSC:

60F15 Strong limit theorems
60G15 Gaussian processes
60G17 Sample path properties
60G18 Self-similar stochastic processes
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