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Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise

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  • Albeverio, Sergio
  • Mastrogiacomo, Elisa
  • Smii, Boubaker

Abstract

We study a reaction–diffusion evolution equation perturbed by a space–time Lévy noise. The associated Kolmogorov operator is the sum of the infinitesimal generator of a C0-semigroup of strictly negative type acting on a Hilbert space and a nonlinear term which has at most polynomial growth, is non necessarily Lipschitz and is such that the whole system is dissipative.

Suggested Citation

  • Albeverio, Sergio & Mastrogiacomo, Elisa & Smii, Boubaker, 2013. "Small noise asymptotic expansions for stochastic PDE’s driven by dissipative nonlinearity and Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2084-2109.
    • Handle: RePEc:eee:spapps:v:123:y:2013:i:6:p:2084-2109
    DOI: 10.1016/j.spa.2013.01.013
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    References listed on IDEAS

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    1. Cerrai, Sandra, 1999. "Differentiability of Markov semigroups for stochastic reaction-diffusion equations and applications to control," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 15-37, September.
    2. Albeverio, S. & Mandrekar, V. & Rüdiger, B., 2009. "Existence of mild solutions for stochastic differential equations and semilinear equations with non-Gaussian Lévy noise," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 835-863, March.
    3. Barbara Forster & Eva Luetkebohmert & Josef Teichmann, 2005. "Absolutely continuous laws of Jump-Diffusions in finite and infinite dimensions with applications to mathematical Finance," Papers math/0509016, arXiv.org, revised Oct 2008.
    4. Albeverio, Sergio & Cebulla, Christof, 2007. "Synchronizability of stochastic network ensembles in a model of interacting dynamical units," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 503-512.
    5. Albeverio, Sergio & Lytvynov, Eugene & Mahnig, Andrea, 2004. "A model of the term structure of interest rates based on Lévy fields," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 251-263, December.
    6. Özkan Fehmi & Schmidt Thorsten, 2005. "Credit risk with infinite dimensional Lévy processes," Statistics & Risk Modeling, De Gruyter, vol. 23(4/2005), pages 281-299, April.
    7. Tuckwell, Henry C. & Jost, Jürgen, 2009. "Moment analysis of the Hodgkin–Huxley system with additive noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4115-4125.
    8. Albeverio, Sergio & Wu, Jiang-Lun & Zhang, Tu-Sheng, 1998. "Parabolic SPDEs driven by Poisson white noise," Stochastic Processes and their Applications, Elsevier, vol. 74(1), pages 21-36, May.
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    Cited by:

    1. Albeverio, Sergio & Smii, Boubaker, 2015. "Asymptotic expansions for SDE’s with small multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 125(3), pages 1009-1031.

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