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

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

2011-05-07

arxiv.org/abs/1105.1480v1

Mathematics

Probability

17 pages

Scientific paper

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.

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