Abstract
This paper has two parts. In part I, existence and uniqueness results are established for solutions of stochastic evolution equations driven both by Brownian motion and by Poisson point processes. Exponential integrability of the solution are also proved. In part II, a large deviation principle is obtained for stochastic evolution equations driven by additive Lévy noise.
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Röckner, M., Zhang, T. Stochastic Evolution Equations of Jump Type: Existence, Uniqueness and Large Deviation Principles. Potential Anal 26, 255–279 (2007). https://doi.org/10.1007/s11118-006-9035-z
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DOI: https://doi.org/10.1007/s11118-006-9035-z