Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach

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Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, background): “†Corresponding author: weiliu@math.uni-bielefeld.de investigated by many authors, see e.g. Kallianpur and Xiong [27], Albeverio et al [2], Mueller et al [43, 44], Applebaum and Wu [3], Mytnik [45], Truman and Wu [58], Hausenblas [25, 26], Mandrekar and Rüdiger [39], Röckner and Zhang [52], Dong et”
Sparse tensor discretizations of high-dimensional parametric and stochastic PDEs* (2011, methodology): “We recapitulate basic properties as needed here and refer to the Appendix of Peszat and Zabczyk (2007) for a more detailed overview.”
Central limit theorem for Markov processes with spectral gap in the Wasserstein metric (2011, methodology): “Our calculations are based on a similar computation made in [29] in the context of an equation with a Lévy noise.”
Two-time-scales hyperbolic–parabolic equations driven by Poisson random measures: Existence, uniqueness and averaging principles (2017, methodology): “The reader is referred to [11, 25] for more detailed descriptions of the stochastic integrals with respect to (cylindrical) Wiener processes and Poisson martingale measures.”
Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise (2011, background): “Our standard reference for Hilbert space-valued Lévy processes is [38].”