H\"{o}lder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses
Probability
2011-05-10 v1 Analysis of PDEs
Abstract
The H\"older continuity of the solution to a nonlinear stochastic partial differential equation arising from one dimensional super process is obtained. It is proved that the H\"older exponent in time variable is as close as to 1/4, improving the result of 1/10 in a recent paper by Li et al [3]. The method is to use the Malliavin calculus. The H\"older continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This H\"older continuity result is sharp since the corresponding linear heat equation has the same H\"older continuity.
Keywords
Cite
@article{arxiv.1105.1480,
title = {H\"{o}lder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses},
author = {Yaozhong Hu and Fei Lu and David Nualart},
journal= {arXiv preprint arXiv:1105.1480},
year = {2011}
}
Comments
17 pages