Research output: Working paper › Preprint

**Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure.** / Brzezniak, Zdzislaw; Hausenblas, Erika.

Research output: Working paper › Preprint

Brzezniak, Z & Hausenblas, E 2010 'Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure'. <http://arxiv.org/abs/1010.5933>

Brzezniak, Z., & Hausenblas, E. (2010). *Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure*. http://arxiv.org/abs/1010.5933

Brzezniak Z, Hausenblas E. Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure. 2010 Oct.

@techreport{db374e9dbb9b4fc1b9451626439ae7d2,

title = "Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by L{\'e}vy noise or Poisson random measure",

abstract = "In this paper we are interested in a reaction diffusion equation driven by Poissonian noise respective L\'evy noise. For this aim we first show existence of a martingale solution for an SPDE of parabolic type driven by a Poisson random measure with only continuous and bounded coefficients. This result is transferred to an parabolic SPDE driven by L\'evy noise. In a second step, we show existence of a martingale solution of reaction diffusion type, also driven by Poissonian noise respective L\'evy noise. Our results answer positively a long standing open question about existence of martingale solutions driven by genuine L\'evy processes. ",

author = "Zdzislaw Brzezniak and Erika Hausenblas",

year = "2010",

month = oct,

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type = "WorkingPaper",

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TY - UNPB

T1 - Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure

AU - Brzezniak, Zdzislaw

AU - Hausenblas, Erika

PY - 2010/10

Y1 - 2010/10

N2 - In this paper we are interested in a reaction diffusion equation driven by Poissonian noise respective L\'evy noise. For this aim we first show existence of a martingale solution for an SPDE of parabolic type driven by a Poisson random measure with only continuous and bounded coefficients. This result is transferred to an parabolic SPDE driven by L\'evy noise. In a second step, we show existence of a martingale solution of reaction diffusion type, also driven by Poissonian noise respective L\'evy noise. Our results answer positively a long standing open question about existence of martingale solutions driven by genuine L\'evy processes.

AB - In this paper we are interested in a reaction diffusion equation driven by Poissonian noise respective L\'evy noise. For this aim we first show existence of a martingale solution for an SPDE of parabolic type driven by a Poisson random measure with only continuous and bounded coefficients. This result is transferred to an parabolic SPDE driven by L\'evy noise. In a second step, we show existence of a martingale solution of reaction diffusion type, also driven by Poissonian noise respective L\'evy noise. Our results answer positively a long standing open question about existence of martingale solutions driven by genuine L\'evy processes.

M3 - Preprint

BT - Martingale solutions for Stochastic Equation of Reaction Diffusion Type driven by Lévy noise or Poisson random measure

ER -