Large deviations are classical topics of study that enjoy great practical application under probability theory. In essence, it studies the properties lie in the tail …
Monte Carlo methods are arguably among the most general purpose numerical tools currently available. There is a relatively long history of the use of large …
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 …
Convex sets in high-dimensional linear spaces are classical objects of study that have long enjoyed rich connections with probability theory. Interest in these connections has …
We prove a moderate deviations principle for the continuous time linear interpolation of discrete time recursive stochastic processes, and then investigate importance sampling schemes based …
We study a general class of mean field interacting particle systems with a finite state space. Particles evolve as exchangeable jump Markov processes, where finite …
In this thesis, we use the large deviations principle to characterize the rate of convergence of the empirical measures of Markov processes. An explicit formula …
This thesis is a large deviations study for the performance of an interacting particle method for rare event estimation. The analysis is restricted to a …
This thesis considers a feed-forward network with a single server station serving jobs with multiple levels of priority. The service discipline is preemptive in that …