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Stochastic partial differential equation driven by stable noise
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  • Published: June 2002

Stochastic partial differential equation driven by stable noise

  • Leonid Mytnik1 

Probability Theory and Related Fields volume 123, pages 157–201 (2002)Cite this article

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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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Authors and Affiliations

  1. Faculty of Industrial Engineering and Management, Technion — Israel Institute of Technology, Haifa 32000, Israel. e-mail: leonid@ie.technion.ac.il, , , , , , IL

    Leonid Mytnik

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  1. Leonid Mytnik
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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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  • Issue Date: June 2002

  • DOI: https://doi.org/10.1007/s004400100180

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Keywords

  • Differential Equation
  • Partial Differential Equation
  • Stochastic Partial Differential Equation
  • Stable Noise
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