Large deviations for solutions of one dimensional Itô equations
Анотація
The large deviations principle for the sequence of stochastic processes \[ \eta _n(t)=x_0+\int _0^t b(n\eta _n(s)) ds+\frac {1}{\varphi (n)}\int _0^t \sigma (n\eta _n(s)) dw(s) \] is proved if the limits of integral means exist for the functions $b(x)\sigma ^{-2}(x)$ and $\sigma ^{-2}(x)$. The rate functional is evaluated.
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