Theory of Probability and Mathematical Statistics
Limit behavior of functionals of solutions of diffusion type equations
G. L. Kulinich, S. V. Kushnirenko, Yu. S. Mishura
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Abstract: The asymptotic behavior as T→∞ of the functionals I(tT) with an appropriate normalizing factor is studied, where I(t)=F(ξ(t))+∫_0^tg(ξ(s))dW(s), t≥0, F is a continuous function, g is a locally square integrable function, ξ is an unstable solution of the Itô stochastic differential equation dξ(t)=a(ξ(t))dt+dW(t), and a is a measurable and bounded function. We find the normalizing factor for the weak convergence of stochastic processes I(tT), t≥0, for certain classes of these equations. The explicit form of the limit processes is established.
Keywords: Diffusion type processes, limit behavior of functionals, unstable solutions of stochastic differential equations
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