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Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Asymptotic behavior of the martingale type integral functionals for unstable solutions to stochastic differential equations

G. L. Kulinich, S. V. Kushnirenko, Yu. S. Mishura

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Abstract: We consider functionals of the type ∫_{0}^{t}g(ξ(s))dW(s), t≥0. Here g is a real valued and locally square integrable function, ξ is a unique strong solution of the Itô stochastic differential equation dξ(t)=a(ξ(t))dt+dW(t), a is a measurable real valued bounded function such that |xa(x)|≤C. The behavior of these functionals is studied as t→∞. The appropriate normalizing factor and the explicit form of the limit random variable are established.

Keywords: Itô stochastic differential equations, unstable solutions, asymptotic behavior of martingale type functionals

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