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