Description
- Abstract:
- Rare events are ones which occur infrequently, sometimes with extremely small probability, but they may nevertheless affect pertinent properties of a system. Such rare events occur in a variety of fields, such as physical chemistry, economics, or operations research, and without specialized computational techniques, simulating them can be prohibitively expensive. In the first part of this thesis we study the performance of splitting techniques for the simulation of rare events. We consider a specific variant of splitting known as RESTART for the numerical approximation of the probability that a process leaves a neighborhood of a metastable point over some long time interval. To do so, we use techniques from Freidlin-Wentzell theory to identify the exponential decay rate of escape probabilities over sequences of increasing time intervals. We use these estimates to establish the asymptotic optimality of the estimator when escape is allowed over long time intervals in the large deviations regime. We also establish the asymptotic optimality of RESTART in the moderate deviations regime for escape probabilities at a fixed terminal time. The second part of this thesis applies the techniques developed in the first part to a class of models known as chemical reaction networks. We study rare events where the process escapes from a rest point, exhibits metastable behavior, or hits a boundary, and we construct explicit subsolutions for different examples of each type. Moreover, we demonstrate that ``complex-balanced'' networks always admit an explicit solution to an associated Hamilton-Jacobi-Bellman equation, and in particular always possess a subsolution which yields an asymptotically optimal estimator.
- Notes:
- Thesis (Ph. D.)--Brown University, 2019
Access Conditions
- Rights
- In Copyright
- Restrictions on Use
- Collection is open for research.
Citation
Snarski, Michael,
"Splitting Techniques for Rare Event Simulation in Chemical Reaction Networks"
(2019).
Applied Mathematics Theses and Dissertations.
Brown Digital Repository. Brown University Library.
https://doi.org/10.26300/dd53-mm74
Relations
Collection:
-
Applied Mathematics Theses and Dissertations
Theses and Dissertations for the Applied Mathematics department....