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A forward-backward SDE from the 2D nonlinear stochastic heat equation

Mathematical Physics and Probability Seminar

A forward-backward SDE from the 2D nonlinear stochastic heat equation
Series: Mathematical Physics and Probability Seminar
Location: Online
Presenter: Alex Dunlap, Courant Institute, NYU

I will discuss a two-dimensional stochastic heat equation in the weak noise regime with a nonlinear noise strength. I will explain how pointwise statistics of solutions to this equation, as the correlation length of the noise is taken to 0 but the noise is attenuated by a logarithmic factor, can be related to a forward-backward stochastic differential equation (FBSDE) depending on the nonlinearity. In the linear case, the FBSDE can be explicitly solved and we recover results of Caravenna, Sun, and Zygouras. Joint work with Yu Gu (CMU).

(https://arizona.zoom.us/j/99811812123)