The main aim of this article is to establish sampling series restoration formulae in for a class of stochastic L 2 -processes which correlation function possesses integral representation close to a Hankel-type transform which kernel is either Bessel function of the first and second kind J ν ,Y ν respectively. The results obtained belong to the class of irregular sampling formulae and present a stochastic setting counterpart of certain older results by Zayed [25] and of recent results by

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... t [13] for J-Bessel sampling and of currently established Y -Bessel sampling results by Jankov Maširević et al. [7] . The approach is twofold, we consider sampling series expansion approximation in the mean-square (or L 2 ) sense and also in the almost sure (or with the probability 1) sense. The main derivation tools are the Piranashvili's extension of the famous Karhunen-Cramér theorem on the integral representation of the correlation functions and the same fashion integral expression for the initial stochastic process itself, a set of integral representation formulae for the Bessel functions of the first and second kind J ν ,Y ν and various properties of Bessel and modified Bessel functions which lead to the so-called Bessel-sampling when the sampling nodes of the initial signal function coincide with a set of zeros of different cylinder functions. Keywords: Almost sure convergence, Bessel functions of the first and second kind J ν ,Y ν , correlation function, harmonizable stochastic processes, Karhunen-Cramér-Piranashvili theorem, Karhunen processes, Kramer's sampling theorem, mean-square convergence, sampling series expansions, sampling series truncation error upper bound, spectral representation of correlation function, spectral representation of stochastic process. MSC(2010): 42C15, 60G12, 94A20.