Existence and uniqueness of mild solutions is established for stochastic evolution equations driven by arbitrary cylindrical Lévy processes under global Lipschitz conditions on the coefficients.
Bichteler.Stochastic integration with jumps
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Develops stochastic integration for predictable processes w.r.t. Lévy basis via decoupling inequalities, reducing to Rajput-Rosiński deterministic theory, with characterization via semimartingale characteristics and Musielak-Orlicz structure.
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Stochastic integration with respect to a L\'evy basis
Develops stochastic integration for predictable processes w.r.t. Lévy basis via decoupling inequalities, reducing to Rajput-Rosiński deterministic theory, with characterization via semimartingale characteristics and Musielak-Orlicz structure.