ASYMPTOTIC BEHAVIOR OF THE INTEGRAL FUNCTIONALS FOR UNSTABLE SOLUTIONS OF ONE-DIMENSIONAL ITO STOCHASTIC DIFFERENTIAL EQUATIONS

We consider the stochastic one-dimensional differential equations with homogeneous drift and unit diffusion. The drift satisfies conditions supplying the unstable property of the unique strong solution. The explicit form of normalizing factor for certain integral functionals of unstable solution is established to provide the weak convergence to the limiting process. As a result we get the new class of limiting processes that are the functionals of Bessel diffusion processes.