The effects of small noise random perturbation for some problems without unique solutions.

Probability Working Seminar
Friday, October 1, 2010 - 15:05
1.5 hours (actually 80 minutes)
Skiles 249
School of Math, Georgia Tech
 We consider the small noise perturbation (in the Ito sense) of a one dimensional ODE. We study the case in which the ODE has not unique solution, but the SDE does. A particular setting of this sort is studied and the properties of the solution are obtained when the noise level vanishes.  We relate this to give an example of a 1-dimensional transport equation without uniqueness of weak solution. We show how by a suitable random noise perturbation, the stochastic equation is well posed and study what the limit is when the noise level tends to zero.