Asymptotic behavior of integral functionals of unstable solutions of one-dimensional Itô stochastic differential equations
Анотація
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.
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