Mathematical Finance and Probability Seminars
Homogenization of a class of one-dimensional nonconvex viscous Hamilton-Jacobi equations with random potential
Atilla Yilmaz - Temple University
Location: Hill 705
Date & time: Tuesday, 19 February 2019 at 11:50AM - 12:55PM
Abstract: I will present joint work with Elena Kosygina and Ofer Zeitouni in which we prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear initial conditions have representations involving exponential expectations of controlled Brownian motion in a random potential. The effective Hamiltonian is the asymptotic rate of growth of these exponential expectations as time goes to infinity and is explicit in terms of the tilted free energy of (uncontrolled) Brownian motion in a random potential. The proof involves large deviations, construction of correctors which lead to exponential martingales, and identification of asymptotically optimal policies.