Nonuniqueness for some stochastic partial differential equations

Stochastics Seminar
Friday, October 9, 2009 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 154 (Unusual time and room)
Carl Mueller – University of Rochester
Yuri Bakhtin
One of the most important stochastic partial differential equations, known as the superprocess, arises as a limit in population dynamics. There are several notions of uniqueness, but for many years only weak uniqueness was known. For a certain range of parameters, Mytnik and Perkins recently proved strong uniqueness. I will describe joint work with Barlow, Mytnik and Perkins which proves nonuniqueness for the parameters not included in Mytnik and Perkins' result. This completely settles the question for strong uniqueness, but I will end by giving some problems which are still open.