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Large deviations for solutions of stochastic equations. (English. Russian original) Zbl 0863.60052
Theory Probab. Appl. 40, No. 4, 660-678 (1995); translation from Teor. Veroyatn. Primen. 40, No. 4, 764-785 (1995).
Let $$D([0,T]; R^d)$$ be a Skorokhod space, $$\mu^\varepsilon(A)=P\{\xi^\varepsilon(\cdot)\in A\}$$, $$A\in {\mathcal B}(D([0,T]; R^d))$$, $$\varepsilon > 0$$, be a family of probability measures, corresponding to the $$d$$-dimensional locally infinitely divisible processes $$\xi^\varepsilon(t)$$, $$t\geq 0$$, $$\varepsilon > 0$$, defined on some filtered probability space. A general principle of large deviations is proved for the family $$\{\mu^\varepsilon$$, $$\varepsilon>0\}$$ in terms of the local characteristics of $$\xi^\varepsilon$$, $$\varepsilon>0$$. Some special cases are discussed in detail.

##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60G48 Generalizations of martingales 60F10 Large deviations