Titlebook: Analysis and Approximation of Rare Events; Representations and Amarjit Budhiraja,Paul Dupuis Book 2019 Springer Science+Business Media, LL

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https://doi.org/10.1007/978-3-031-04787-9s in a chemical reaction network; and exceedance of a regulatory threshold in a model for pollution in a waterway. In previous chapters we have described how large deviation theory gives approximations for such quantities. The approximations take the form of logarithmic asymptotics, i.e., exponential decay rates.

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Abel Kinoti Meru,Mary Wanjiru Kinotiultiplicative 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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CHURL

General Theory As is usual, we will refer to such a space as a .. The metric of . is denoted by .(., .), and expectation with respect to . by .. The theory of large deviations focuses on random variables . for which the probabilities . converge to 0 exponentially fast for a class of Borel sets ..

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Models with Special Featuresame type, and large deviations for the empirical measure of a Markov chain. These chapters thus consider models that are both standard and fairly general for each setting. In this chapter we consider discrete time models that are somewhat less standard, with the aim being to show how the weak conver

FEMUR

Representations for Continuous Time Processespresentations in this setting follows from a straightforward application of the chain rule. The only significant issue is to decide on the ordering used for the underlying “driving noises” when the chain rule is applied, since controls are allowed to depend on the “past,” which is determined by this

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Large and Moderate Deviations for Finite Dimensional Systemsonal jump-diffusions. We will consider only Laplace principles rather than uniform Laplace principles, since, as was noted in Chap. ., the extension from the nonuniform to the uniform case is straightforward. The first general results on large deviation principles for jump-diffusions of the form con

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