Large deviations in power zones in the approximation by the Poisson law

Large deviations for integer centered poisson approximation

“…Moreover, in [4], Ale~kevi6iene and Statulevi~ius considerably weakened (S), replacing k! by (k I)l+v.…”

“…Estimates under condition (P) were considered in [9], [18], [20] and under (S) in [2]- [4]. Moreover, in [4], Ale~kevi6iene and Statulevi~ius considerably weakened (S), replacing k!…”

On a centered Poisson approximation

“…Large deviations and integral estimates under condition (P) were considered in [12], [22], [23], [29], [30] and, under (S), in [3]- [5]. (Note that, in [5], Ale~kevi~ien6 and Statulevi~ius obtained results under a considerably weaker form of (S), where k! was replaced by (k!)l+Y.)…”

“…Large deviations under conditions (S) or (P) were considered in [3], [5], [12], [16], [30]. In all these papers the approximating distribution (or measure) depended on the cumulants of F only.…”

“…In recent years, limit theorems have been marked by numerous papers on Poisson approximations; see, for example, [1]- [5], [7], [9], [11], [13], [15], [17]- [24], [29]- [33] and the references therein. We can state that, in this field, an overwhelming majority of research is following traditions established by the pioneering papers of Prokhorov [32], Le Cam [26], Grigelionis [20], and Franken [19].…”