The Central Limit Theorem for Weakly Dependent Banach-Valued Variables

Central Limit Theorem in Lebesgue-Riesz spaces for weakly dependent random sequences

“…We intend to generalize in this report the foregoing results [12], [26] relative the CLT in the space L(2, T ) into more general case of the space L(p, T ) when the source random sequence {ξ i (t)} forms relative the index i a sequence satisfying aside from certain moment assumptions the strong mixing condition.…”

“…The CLT in different Banach spaces, or more generally, in linear topological ones, is devoted the extensive literature, see e.g. [1], [2], [7], [10], [11], [12], [17], [22], [23], [24], [25], [26], [27], [28], [37], [38], [41], [44]. As a rule, in these works was investigated the case when the r.f.…”

“…The case of CLT in Lebesgue-Riesz spaces for weakly dependent variables under super strong mixing condition is considered in [12], [26].…”

“…The non-asymptotical estimation for sums of weakly dependent r.v. is represented in particular in [11], [12], [42]. We will apply the estimate belonging to S.A.Utev [43].…”

Averaging of random variables and fields

“…These spaces are complete Banach functional rearrangement invariant; they are investigated in many works, see e.g. [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. It is important for us in particular to note that there is exact of course up to finite multiplicative constant interrelations under certain natural conditions on the generating function between belonging the r.v.…”