STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY LÉVY SPACE-TIME WHITE NOISE By

@inproceedings{Lkka1996STOCHASTICPD,
  title={STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS DRIVEN BY L{\'E}VY SPACE-TIME WHITE NOISE By},
  author={Arne L\okka and Bernt \Oksendal},
  year={1996}
}
In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d ≤ 3, then this solution can be represented as a classical random field in L 2 (µ), where µ is the probability law of… CONTINUE READING

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References

Publications referenced by this paper.
Showing 1-10 of 21 references

The heat equation with Lévy noise

  • C. Mueller
  • Stochastic Process . Appl .
  • 1998

On an analog of stochastic integral and Wick calculus in non - Gaussian infinite dimensional analysis

  • N. A. Kachanowsky
  • Methods Funct . Anal . Topology
  • 1997

Dual Appell systems in Poissonian analysis

  • G. F. Us
  • Methods Funct . Anal . Topology
  • 1995

How to generalize white noise analysis to non - Gaussian spaces

  • S. Albeverio, Y. G. Kondratiev, L. Streit
  • Dynamics of Complex and Irregular Systems
  • 1993

Stochastic differential equations involving positive noise

  • T. Lindstrøm, B. Øksendal, J. Ubøe
  • Stochastic Analysis
  • 1991

The vacuum of the Høegh - Krohn model as a generalized white noise functional

  • S. Albeverio, T. Hida, J. Potthoff, L. Streit
  • Phys . Lett . B
  • 1989

Calculus on Gaussian and Poisson white noises

  • Y. Itô, I. Kubo
  • Nagoya Math . J .
  • 1988

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