@article{ECP1333,
author = {Giuseppe Da Prato and Arnaud Debussche and Luciano Tubaro},
title = {A modified Kardar-Parisi-Zhang model},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {12},
year = {2007},
keywords = {Stochastic partial differential equations; white noise; invariant measure; Wick product},
abstract = {A one dimensional stochastic differential equation of the form \[dX=A X dt+\tfrac12 (-A)^{-\alpha}\partial_\xi[((-A)^{-\alpha}X)^2]dt+\partial_\xi dW(t),\qquad X(0)=x\] is considered, where $A=\tfrac12 \partial^2_\xi$. The equation is equipped with periodic boundary conditions. When $\alpha=0$ this equation arises in the Kardar-Parisi-Zhang model. For $\alpha\ne 0$, 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 of a strong solution provided $\alpha>\frac18$.},
pages = {no. 42, 442-453},
issn = {1083-589X},
doi = {10.1214/ECP.v12-1333},
url = {http://ecp.ejpecp.org/article/view/1333}}