Asymptotic behaviour of the convolution tail of distributions each having a first or second order regularly varying tail
Suppose X, Y are i.i.d. positive r.v.'s with infinite mean. We study the asymptotic behaviour of P(X + Y > x ) as x-»oo in case 1 F(x) and 1 G(x) are regularly varying at infinity. As an application of the results we evaluate the asymptotic behaviour of the tail d.f. of the convolution of two stable d.f.'s on R^ each of index between 0 and Vi. K e y w o r d s : regulär Variation, convolution, stable distribution.