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 evolution equations driven by arbitrary cylindrical L\'evy processes
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.
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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.