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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.

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