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Published in:
2019 | OriginalPaper | Chapter
9. Abstract Sufficient Conditions for Large and Moderate Deviations in the Small Noise Limit
Authors : Amarjit Budhiraja, Paul Dupuis
Published in: Analysis and Approximation of Rare Events
Publisher: Springer US
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Abstract
In this chapter we use the representations derived in Chap. 8 to study large and moderate deviations for stochastic systems driven by Brownian and/or Poisson noise, and consider a “small noise” limit, as in Sects. 3.2 and 3.3. We will prove general abstract large deviation principles, and in later chapters apply these to models in which the noise enters the system in an additive and independent manner (In our terminology, this includes systems with multiplicative noise, namely settings in which the noise term is multiplied by a state-dependent coefficient). For these systems, one can view the mapping that takes the noise into the state of the system as “nearly” continuous, and it is this property that allows a unified and relatively straightforward treatment.