Finite difference equations and convergence rates in the central limit theorem

• Autorzy: Lindhagen L.
• Języki publikacji: EN

Abstrakty

EN

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)ǁ_Lp(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.

Słowa kluczowe

EN

Finite difference equations; central limit theorem; convergence rate; interpolation theory; Fourier multipliers; Besov spaces; signed probability

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2007
• Tom: Vol. 27, Fasc. 2
• Strony: 153--166
• Opis fizyczny: Bibliogr. 29 poz.

Twórcy

autor

Lindhagen L.

• Saab Systems, S:t Olofsgatan 9A, 75321 Uppsala, Sweden

Bibliografia

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