Abstract
The Holder continuity of the solution Xt(x) to a nonlinear stochastic partial differential equation (see (1.2) below) arising from one dimensional superprocesses is obtained. It is proved that the Holder exponent in time variable is arbitrarily close to 1/4, improving the result of 1/10 in Li et al. (to appear on Probab. Theory Relat. Fields.). The method is to use the Malliavin calculus. The Holder continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This Holder continuity result is sharp since the corresponding linear heat equation has the same Holder continuity.
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