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Hyperbolic type stochastic evolution equations with Lévy noise. (English) Zbl 1276.60065
Stochastic evolution equations (SEEs) of hyperbolic type driven by Lévy noise are considered. The authors study the existence and uniqueness for solutions of linear and nonlinear SEEs. They combine the method for solving deterministic evolution equations of second order in time with the iteration techniques for SEEs. An energy equality for nonlinear equations is established in the paper.
The techniques used are based on the variational framework and the solutions are considered to be weak solution.
As examples, these results are applied to stochastic wave-type equations with jumps.

MSC:
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35L90 Abstract hyperbolic equations
74G25 Global existence of solutions for equilibrium problems in solid mechanics (MSC2010)
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