TY - JOUR
T1 - Paracontrolled calculus and Funaki–Quastel approximation for the KPZ equation
AU - Hoshino, Masato
N1 - Funding Information:
This work was supported by JSPS KAKENHI , Grant-in-Aid for JSPS Fellows, JP16J03010 . The author would like to thank Professor T. Funaki for leading him to the problem discussed in the present paper. The author also thanks anonymous referees for their helpful remarks.
Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2018/4
Y1 - 2018/4
N2 - In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel (2015), which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the Cole–Hopf solution of the KPZ equation with extra term [Formula presented]t. On the other hand, Gubinelli and Perkowski (2017) gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus.
AB - In this paper, we consider the approximating KPZ equation introduced by Funaki and Quastel (2015), which is suitable for studying invariant measures. They showed that the stationary solution of the approximating equation converges to the Cole–Hopf solution of the KPZ equation with extra term [Formula presented]t. On the other hand, Gubinelli and Perkowski (2017) gave a pathwise meaning to the KPZ equation as an application of the paracontrolled calculus. We show that Funaki and Quastel's result is extended to nonstationary solutions by using the paracontrolled calculus.
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U2 - 10.1016/j.spa.2017.07.001
DO - 10.1016/j.spa.2017.07.001
M3 - Article
AN - SCOPUS:85027455941
SN - 0304-4149
VL - 128
SP - 1238
EP - 1293
JO - Stochastic Processes and their Applications
JF - Stochastic Processes and their Applications
IS - 4
ER -