Abstract
The solution of the stochastic equation X(t) = x 0 + b∫ t0 sign(X(s))|X(s)|γ ds + w(t); where w(t) is the Wiener process, the constant b ≠ 0, and γ ∈ (0; 1]; is considered. The local principle of large deviations for the sequence of processes \( {X}_n(t)=\frac{X(nt)}{n^{\alpha }},\alpha >1/2 \), is proved. The form of the rate function is found.
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 4, pp. 457–471, September–December, 2015.
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Logachov, A.V. The local principle of large deviations for solutions of Itô stochastic equations with quick drift. J Math Sci 218, 28–38 (2016). https://doi.org/10.1007/s10958-016-3008-6
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DOI: https://doi.org/10.1007/s10958-016-3008-6