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We derive in this preprint the moment and exponential tail estimates,sufficient conditions for the Non-Central Limit Theorem (NCLT) in the ordinaryone-dimensional space as well as in the space of continuous functions for theproperly (natural) normalized multi-indexed sums of function of randomvariables, processes or fields (r.f.), on the other words V-statistics,parametric, in general case.  We construct also some examples in order to show the exactness of obtainedestimates.  We will use the theory of the so-called degenerate approximation of thefunctions of several variables as well as the theory of  Grand Lebesgue Spaces (GLS) of measurable functions (random variables).

Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields