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arXiv · 1105.1480

Hölder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses

Yaozhong Hu·Fei Lu·David Nualart
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Abstract

The Hölder continuity of the solution to a nonlinear stochastic partial differential equation arising from one dimensional super process is obtained. It is proved that the Hölder 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 Hölder continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This Hölder continuity result is sharp since the corresponding linear heat equation has the same Hölder continuity.

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Yaozhong Hu, Fei Lu, David Nualart. 2011-05-07. Hölder Continuity of the Solution for a Class of Nonlinear SPDE Arising from One Dimensional Superprocesses. https://arxiv.org/abs/1105.1480

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