Probability Seminar
Thursday, February 4, 2021, 3:15pm, Virtual
Alex Dunlap (Courant Institute, Mathematics)
A forward-backward SDE from the 2D nonlinear stochastic heat equation
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 the log-normal behavior proved by Caravenna, Sun, and Zygouras. Joint work with Yu Gu (CMU).

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