On the equivalence of Gaussian measures corresponding to the solutions of stochastic differential equations

Let Gaussian measures $P_1$ and $P_2$ correspond to the solutions of stochastic differential equations $\mathscr P_i\xi(t)=\xi^\ast(t)$, $i=1,2,\dots$ in bounded domain $T\subseteq R^d$, where $\mathscr P_1$ and $\mathscr P_2$ are some elliptic operators of order $2l$. It is shown that $P_1$ and $P_2$ are equivalent if $2l-q>d/2$ where $q$ is the order of $\mathscr P_2-\mathscr P_1$.