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Large deviations in the piecewise linear approximation of Gaussian processes with stationary increments

Part of: Limit theorems Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Oleg Seleznjev
Oleg Seleznjev*
Affiliation:
Moscow State University
*
∗ Postal address: Faculty of Mathematics and Mechanics, Moscow State University, 119 899 Moscow, Russia.
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Abstract

We consider the piecewise linear interpolation of Gaussian processes with continuous sample paths and stationary increments. The interrelation between the smoothness of the incremental variance function, d(t – s) = E[(X(t) – X(s))2], and the interpolation errors in mean square and uniform metrics is studied. The method of investigation can also be applied to the analysis of different methods of interpolation. It is based on some limit results for large deviations of a sequence of Gaussian non-stationary processes and related point processes. Non-stationarity in our case means mainly the local stationary condition for the sequence of correlation functions rn(t,s), n = 1, 2, ···, which has to hold uniformly in n. Finally, we discuss some examples and an application to the calculation of the distribution function of the maximum of a continuous Gaussian process with a given precision.

Keywords

MAXIMUM OF NON-STATIONARY GAUSSIAN PROCESSESPOINT PROCESSINTERPOLATION OF REALIZATION

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G15: Gaussian processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 28 , Issue 2 , June 1996 , pp. 481 - 499
Copyright
Copyright © Applied Probability Trust 1996 

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Footnotes

Supported by the Swedish Natural Science Research Council, contract 927620 NFR 3741–307.

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