Stochastic Control Approach to KPZ equation
- Series
- Stochastics Seminar
- Time
- Thursday, April 25, 2013 - 15:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Sergio Almada – UNC Chapel Hill
The Kardar-Parisi-Zhang(KPZ) equation is a non-linear stochastic partial
di fferential equation proposed as the scaling limit for random growth
models in physics. This equation is, in standard terms, ill posed and
the notion of solution has attracted considerable attention in recent
years. The purpose of this talk is two fold; on one side, an
introduction to the KPZ equation and the so called KPZ universality
classes is given. On the other side, we give recent results that
generalize the notion of viscosity solutions from deterministic PDE to
the stochastic case and apply these results to the KPZ equation. The
main technical tool for this program to go through is a non-linear
version of Feyman-Kac's formula that uses Doubly Backward Stochastic
Differential Equations (Stochastic Differential Equations with times
flowing backwards and forwards at the same time) as a basis for the
representation.