logo_acta

Acta Mathematica Vietnamica

ON ITO STOCHASTIC INTEGRAL WITH RESPECT TO VECTOR STABLE RANDOM MEASURES

icon-email DANG HUNG THANG

Abstract

Let $Z_p$ be a vector $p$-stable random measure with values in a $q$-smoothable Banach space, where $p > q$ if $p < 2$ and $q = 2$ if $p = 2$. It is shown that the stochastic integral $\int_0^1udZ_p$ can be defined for processes $u$ which are non-anticipating with respect to $Z_p$.