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Finite difference equations and convergence rates in the central limit theorem

Lindhagen L.

Probability and Mathematical Statistics

2007

Vol. 27, Fasc. 2

153--166

We apply the theory of finite difference equations to the central limit theorem, using interpolation of Banach spaces and Fourier multipliers. Let S*n be a normalized sum of i.i.d. random vectors, converging weakly to a standard normal vector N. When does ǁEg (x + S*n) -E g (X + N)ǁLp(dx)tend to zero at a specified rate? We show that, under moment conditions, membership of g in various Besov spaces is often sufficient and sometimes necessary. The results extend to signed probability.

On a Compact Extension

Hofmanová P.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

1999

Vol. 6

29--31