Variational solutions of stochastic partial differential equations with cylindrical Lévy noise

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Abstract

In this article, the existence of a unique solution in the variational approach of the stochastic evolution equation
$$\dX(t) = F(X(t)) \dt + G(X(t)) \dL(t)$$
driven by a cylindrical Lévy process L is established. The coefficients F and G are assumed to satisfy the usual monotonicity and coercivity conditions. The noise is modelled by a cylindrical Lévy processes which is assumed to belong to a certain subclass of cylindrical Lévy processes and may not have finite moments.
Original languageEnglish
Number of pages20
JournalDiscrete and continuous dynamical systems-Series b
Publication statusAccepted/In press - 24 Apr 2020

Keywords

  • cylindrical Lévy processes
  • stochastic partial differential equations
  • multiplicative noise
  • variational solutions
  • Stochastic integration

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