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

RENIN

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天然熱噴泉

雀斑

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 convergence methodology can be adapted.

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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 ordering.

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Performance of an IS Scheme Based on a Subsolution .. Two types of events were emphasized: those that are described by process behavior on a bounded time interval (finite-time problems) and those that concern properties of the process over unbounded time horizons (e.g., exit probability problems).

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