Domain of attraction of the quasi-stationary distributions for the Ornstein-Uhlenbeck process

Let (X-t) be a one-dimensional Ornstein-Uhlenbeck process with initial dens ity function f : R+ --> R+, which is a regularly varying function with expo nent -(1 + eta), eta is an element of (0, 1). We prove the existence of a p robability measure nu with a Lebesgue density, depending on eta, such that for every A is an element of B(R+): lim(t-->infinity) P-f(X-t is an element of A \ T-0(X) > t) = nu(A).