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1052 CSÁKI, E., CSÖRGÖ, M., FÖLDES, A. and RÉVÉSZ, P., Strong approximation of additive functionals, J. Theoret. Probab. 5 (1992), 679-706. MR 93k :60073 Strong

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CSÖRGő, M. and RÉVÉSZ, P., Strong approximations in probability and statistics , Akadémiai Kiadó, Budapest; Academic Press, New York, 1981. MR 84d :60050 Strong approximations in probability and statistics

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Abstract  

We describe the functions from Nikol’skii class in terms of behavior of their Fourier coefficients. Results for series with general monotone coefficients are presented. The problem of strong approximation of Fourier series is also studied.

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Summary Some topics of our twenty some years of joint work is discussed. Just to name a few; joint behavior of the maximum of the Wiener process and its location, global and local almost sure limit theorems,  strong approximation of the planar local time difference, a general Strassen type theorem, maximal local time on subsets.

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References [1] Zhang , L. X. 2002 Strong approximation theorems for sums of random variables when extreme terms are excluded

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. 1997 Strong approximation theorems for geometrically weighted random series and their applications Ann. Probab. 25 1621 – 1635 10.1214/aop/1023481105

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Abstract  

We verify a newer version of a certain embedding theorem pertaining to the relation being between strong approximation and a certain wide class of continuous functions. We also show that a new class of numerical sequences defined in this paper is not comparable to the class defined by Lee and Zhou, which is one of the largest among the classes being extensions of the class of monotone sequences.

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