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Moderate deviation principles for stochastic differential equations with jumps. (English) Zbl 1346.60026

The paper deals with moderate deviation problems for stochastic dynamical systems such as finite- and infinite-dimensional SDEs with jumps. For simplicity, the setting considers only the noise in terms of a Poisson random measure without the Brownian component. Moderate deviation problem means that probabilities of deviations have a smaller order than in large deviation theory. In this case, the deviation order is \(n^{1/2}a_n,\) which is of lower order than \(n,\) where the \(a_n\)-rate function has a quadratic form. The moderate deviation problems bridge the gap between a central limit approximation and a large deviations approximation, since \(a_n\to+\infty\) as slowly as desired.

MSC:

60F10 Large deviations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60G57 Random measures
60J75 Jump processes (MSC2010)
60J25 Continuous-time Markov processes on general state spaces
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References:

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