Colloquium

Thursday, Oct. 23, 2007

4:00 PM, BAC 219

Speaker: Marco Pollanen, Trent University, Peterborough, Ontario, Canada

Host: Vasant Waikar

Title: Generalized Weyl-Sequences and Quasi-Monte Carlo Methods

Abstract:

Many complex mathematical problems can be solved by Monte Carlo or

Quasi-Monte Carlo (QMC) methods. Thus, there are many algorithms for

directly generating pseudo and quasi-random sequences, almost all of

which are for the uniform distribution. However, many applications

require non-uniform pseudo or quasi-random sequences. For example, QMC

integration is often applied to integrands on unbounded domains with

non-uniform probability measures, integrals for which there is little

theoretical validation. In this talk we will introduce a

group-theoretic methods to generate some non-uniform deterministic

Weyl-like (quasi-random) sequences, as well as a new importance

sampling technique, which can be used with these group-theoretic

sequences to create QMC integration rules with a high asymptotic order

of convergence. We will also discuss a related group-theoretic method

to generate some non-uniform pseudo-random sequences.

BRIEF BIO:

Marco Pollanen is an assistant professor in the Department of

Mathematics at Trent University in Peterborough, Ontario, Canada. He

holds a Ph.D. and a M.Sc. in mathematics from the University of

Toronto and a B.Sc. in mathematics from Carleton University. His

research areas include mathematical finance, numerical analysis,

applied probability and mathematical knowledge management.