Event Detail

Event Type: 
Department Colloquium
Friday, February 2, 2007 - 07:00
Kidd 364

Speaker Info

U. Utah

Consider the classical heat equation in dimension d, and formally replace the external forcing term by white noise. The resulting "stochastic PDE" (SPDE, for short) is the so-called stochastic heat equation. It has been known for some time that the stochastic heat equation suffers from a "curse of dimensionality": It has function solutions if and only if the ambient dimension is one. First we present a rigorous formulation of this SPDE, and explain why it has function solutions in only one dimension. Then, we discuss some newly-found connections between systems of solutions and classical notions from geometric measure theory [joint work with Robert Dalang and Eulalia Nualart]. Time permitting, we also address the mentioned curse of dimensionality, in greater length, by presenting an unexpected connection to classical probabilistic potential theory and the theory of local times [joint work with Mohammud Foondun and Eulalia Nualart].