ASYMPTOTIC BEHAVIOR OF INTEGRAL FUNCTIONALS OF UNSTABLE SOLUTIONS OF ONE-DIMENSIONAL IT? STOCHASTIC DIFFERENTIAL EQUATIONS

摘要

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