Mathematical Finance and Probability Seminars (Since covid these events are taking place online.)

The Probability of a Rare Event

Tuesday, March 20, 2012 at 11:00am - 12:00pm

Speaker: Leila Setayeshgar, Brown University

We begin by considering a feed-forward network with a single server station serving jobs with multiple levels of priority. The service discipline is preemptive in that the server always serves a job with the current highest priority level. For this system with discontinuous dynamics, we show (outline) that the family of scaled state processes satisfy the sample path large deviations principle using a weak convergence argument. In the special case where the jobs have two different levels of priority, we explicitly identify the exponential decay rate of the probability a rare event, namely, the “total population overflow” associated to the feed-forward network. We then use importance sampling – a variance reduction technique – efficient for rare event probabilities to simulate the exact probability of interest. We conclude by confirming our theoretical results with numerical simulations. (This is work under the supervision of Prof. Hui Wang.)

Speaker: Leila Setayeshgar, Brown University

Location   Hill 705