Abstract
In previous chapters we developed and applied representations for the large deviation analysis of discrete time processes. The derivation of useful representations 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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- 1.
For special cases, one can consider the infimum of a smaller class (e.g., feedback controls), a result that is sometimes of interest.
- 2.
We will use the terms “Brownian motion” and “Wiener process” interchangeably.
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Budhiraja, A., Dupuis, P. (2019). Representations for Continuous Time Processes. 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_8
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DOI: https://doi.org/10.1007/978-1-4939-9579-0_8
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