Hermite polynomicals and the product of Gaussian measures


Zoran Ivković




Let $\{\eta(t),\ t>0\}$, be a Gaussian martingale and $H_p(\eta(t_1),\dots,\eta(t_p))$ be the Hermite polynomial. In this paper it is proved that $\Delta^pH_p(\eta)=\prod_1^n[\eta(t_i+h_i)-\eta(t_i)]$ and this permits the defining of the multiple Ito-Rozanov stochastic integral by \[ ıt_0^ıfty\dotsıt_0^ıftyǎrphi(t_1,\dots,t_p)d^pH(\eta). \]