玷污
发表于 2025-3-23 13:18:24
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.
reflection
发表于 2025-3-23 15:13:18
http://reply.papertrans.cn/16/1562/156153/156153_12.png
荧光
发表于 2025-3-23 20:40:56
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.
船员
发表于 2025-3-24 00:07:25
http://reply.papertrans.cn/16/1562/156153/156153_14.png
CHURL
发表于 2025-3-24 04:44:31
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 ..
滴注
发表于 2025-3-24 07:22:24
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
发表于 2025-3-24 11:10:33
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
沙文主义
发表于 2025-3-24 17:48:04
http://reply.papertrans.cn/16/1562/156153/156153_18.png
分发
发表于 2025-3-24 21:30:47
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
商谈
发表于 2025-3-25 00:09:14
http://reply.papertrans.cn/16/1562/156153/156153_20.png