Abstract.
We construct a weak solution to the stochastic partial differential equation driven by a one sided, α-stable noise without negative jumps. We prove the weak existence of the solution for parameters . The facts that, for is not a Lipschitz function, and is not a Gaussian noise require the development of new methods, which we believe are of independent interest. We also show that when the above equation gives an alternative description of super-Brownian motion with stable branching mechanism.
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Received: 31 March 2001 / Revised version: 23 July 2001 / Published online: 17 May 2002
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Mytnik, L. Stochastic partial differential equation driven by stable noise. Probab. Theory Relat. Fields 123, 157–201 (2002). https://doi.org/10.1007/s004400100180
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DOI: https://doi.org/10.1007/s004400100180