TY - JOUR

T1 - Approximation of convolutions of multi-dimensional symmetric distributions by accompanying laws

AU - Zaitsev, A. Yu

PY - 1992/8/1

Y1 - 1992/8/1

N2 - Let F be a symmetric k-dimensional probability distribution, whose characteristic function {Mathematical expression} satisfies for all t ∈Rk the inequality {Mathematical expression} ≥ -1 + α, where 0 < α < 2. Let n be an arbitrary natural number, let Fn be the n-fold convolution of the distribution F with itself, and let e(nF) be the accompanying infinitely divisible distribution with characteristic function exp(n( {Mathematical expression} -1)). It is proved that the uniform distance ρ(·,·) between corresponding distribution functions admits estimate ρ(Fn,e(nF))≤c1(k)(n-1+exp(-nα+cℓkℓn3n)), where c1(k) depends only on the dimension k, while c2is an absolute constant.

AB - Let F be a symmetric k-dimensional probability distribution, whose characteristic function {Mathematical expression} satisfies for all t ∈Rk the inequality {Mathematical expression} ≥ -1 + α, where 0 < α < 2. Let n be an arbitrary natural number, let Fn be the n-fold convolution of the distribution F with itself, and let e(nF) be the accompanying infinitely divisible distribution with characteristic function exp(n( {Mathematical expression} -1)). It is proved that the uniform distance ρ(·,·) between corresponding distribution functions admits estimate ρ(Fn,e(nF))≤c1(k)(n-1+exp(-nα+cℓkℓn3n)), where c1(k) depends only on the dimension k, while c2is an absolute constant.

UR - http://www.scopus.com/inward/record.url?scp=0012910695&partnerID=8YFLogxK

U2 - 10.1007/BF01362793

DO - 10.1007/BF01362793

M3 - Article

AN - SCOPUS:0012910695

VL - 61

SP - 1859

EP - 1872

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -