A modified Kardar-Parisi-Zhang model

Giuseppe Da Prato, Arnaud Debussche, Luciano Tubaro
2007 Electronic Communications in Probability  
A one dimensional stochastic differential equation of the form dX = The equation is equipped with periodic boundary conditions. When α = 0 this equation arises in the Kardar-Parisi-Zhang model. For α = 0, this equation conserves two important properties of the Kardar-Parisi-Zhang model: it contains a quadratic nonlinear term and has an explicit invariant measure which is gaussian. However, it is not as singular and using renormalization and a fixed point result we prove existence and uniqueness
more » ... ence and uniqueness of a strong solution provided α > 1 8 .
doi:10.1214/ecp.v12-1333 fatcat:oorw3yk7jnbkbdq6eadizdgyku