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



Large deviations for solutions of one dimensional Itô equations

A. V. Logachov

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Abstract: The large deviations principle for the sequence of stochastic processes η_n(t)=x_0+∫_0^tb(nη_n(s))ds+1/φ(n)∫_0^tσ(nη_n(s))dw(s) is proved if the limits of integral means exist for the functions b(x)σ^{-2}(x) and σ^{-2}(x). The rate functional is evaluated.

Keywords: Large deviations, rate functional, stochastic differential equation

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