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The Burgers superprocess

Author

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  • Bonnet, Guillaume
  • Adler, Robert J.

Abstract

We define the Burgers superprocess to be the solution of the stochastic partial differential equation where t>=0, , and W is space-time white noise. Taking [gamma]=0 gives the classic Burgers equation, an important, non-linear, partial differential equation. Taking [lambda]=0 gives the super-Brownian motion, an important, measure valued, stochastic process. The combination gives a new process which can be viewed as a superprocess with singular interactions. We prove the existence of a solution to this equation and its Hölder continuity, and discuss (but cannot prove) uniqueness of the solution.

Suggested Citation

  • Bonnet, Guillaume & Adler, Robert J., 2007. "The Burgers superprocess," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 143-164, February.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:2:p:143-164
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    References listed on IDEAS

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    1. Gyöngy, István, 1998. "Existence and uniqueness results for semilinear stochastic partial differential equations," Stochastic Processes and their Applications, Elsevier, vol. 73(2), pages 271-299, March.
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    Cited by:

    1. Englezos, Nikolaos & Frangos, Nikolaos E. & Kartala, Xanthi-Isidora & Yannacopoulos, Athanasios N., 2013. "Stochastic Burgers PDEs with random coefficients and a generalization of the Cole–Hopf transformation," Stochastic Processes and their Applications, Elsevier, vol. 123(8), pages 3239-3272.

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