Theory of Probability and Mathematical Statistics
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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