Quenched asymptotics for Brownian motion in a Gaussian potential

Series: 
Stochastics Seminar
Thursday, March 28, 2013 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
University of Tennessee
 Recall that the notion of generalized function is introduced for the functions that are not defined point-wise, and is given as a linearfunctional over test functions. The same idea applies to random fields.In this talk, we study the long term asymptotics for the quenchedexponential moment of V(B(s)) where B(s) is d-dimensional Brownian motion,V(.) is a generalized Gaussian field. We will discuss the solution to anopen problem posed by Carmona and Molchanov with an answer different fromwhat was conjectured; the quenched laws for Brownian motions inNewtonian-type potentials, and in the potentials driven by white noise orby fractional white noise.