formula

$E(|X_t|^p)&=&\int_0^{\infty}py^{p-1}P(|X_t|>y)dy\\ &\leq &\int_0^{\infty}py^{p-1}\exp(-py)E(\exp(|pX_t|))dy\\ &\leq & p(E(\exp(pX_t))+E(\exp(-pX_t))\int_0^{\infty}y^{p-1}\exp(-py)dy\\ &\leq & p\bigg(1+\frac{p}{2t(2-p)}+\frac{\Gamma (p/2+1)}{(2t)^{p/2+2}}\bigg)\frac{\Gamma (p)}{p^p}\\ &\leq & \bigg(1+\frac{p}{2(2-p)}+\Gamma (p/2+1)\bigg)\frac{\Gamma (p)}{p^{p-1}}<\infty \quad (t\geq 1)$