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.
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In our terminology, this includes systems with multiplicative noise, namely settings in which the noise term is multiplied by a state-dependent coefficient.
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Budhiraja, A., Dupuis, P. (2019). Abstract Sufficient Conditions for Large and Moderate Deviations in the Small Noise Limit. In: Analysis and Approximation of Rare Events. Probability Theory and Stochastic Modelling, vol 94. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9579-0_9
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DOI: https://doi.org/10.1007/978-1-4939-9579-0_9
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