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A strong approximation for some non-stationary complex Gaussian processes

Published online by Cambridge University Press:  14 July 2016

Peter Breuer
Peter Breuer*
Affiliation:
Institute for Psychology of the Hungarian Academy of Sciences
*
∗Postal address: Institute for Psychology of the Hungarian Academy of Sciences, H–1394 Budapest Pf. 398, Hungary.
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Abstract

A strong approximation theorem is proved for some non-stationary complex-valued Gaussian processes and an explicit rate of convergence is achieved. The result answers a problem raised by S. Csörgő.

Keywords

EMPIRICAL CHARACTERISTIC PROCESSSNAKE THEOREMFERNIQUE INEQUALITYGAUSSIAN APPROXIMATION
Type
Research Papers
Information
Journal of Applied Probability , Volume 18 , Issue 2 , June 1981 , pp. 390 - 402
Copyright
Copyright © Applied Probability Trust 

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References

[1] Csörgo, S. (1978) Limit behaviour of the empirical characteristic function. Ann. Prob. 8.Google Scholar
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[5] Kent, J. T. (1975) A weak convergence theorem for the empirical characteristic function. J. Appl. Prob. 12, 515–523.Google Scholar