Recipients will offer public lectures on the prize-winning papers which were selected from the Canadian Journal of Mathematics (1994-95). Sponsored by the Canadian Mathematical Society and The Fields Institute for Research in Mathematical Sciences.
2:30 - 2:45 p.m. | Introduction and Comments |
Dr. Katherine Heinrich, Canadian Mathematical Society | |
2:45 - 3:30 p.m. | Public Lecture |
Dr. Henri R. Darmon, Mathematics and Statistics, McGill University |
3:30 - 3:45 p.m. | Break and Refreshments |
3:45 - 4:30 p.m. | Public Lecture |
Dr. Steven N. Evans, Statistics, University of
California, Berkeley Dr. Edwin A. Perkins, Mathematics, University of British Columbia |
We first consider a competition model in which inter-species collisions may result in casualties on both sides. Using a Girsanov approach, we obtain existence and uniqueness of the appropriate martingale problem in one dimension. In two and three dimensions we establish existence only. However, we do show that, in three dimensions, any solution will not be absolutely continuous with respect to the law of two independent super-Brownian motions. Although the supports of two independent super-Brownian motions collide in dimensions four and five, we show that there is no solution to the martingale problem in these cases.
We next study a predation model in which collisions only affect the ``prey'' species. Here we can show both existence and uniqueness in one, two and three dimensions. Again, there is no solution in four and five dimensions. As a tool for proving uniqueness, we obtain a representation of martingales for a super-process as stochastic integrals with respect to the related orthogonal martingale measure.