Existence, Uniqueness and Regularity of Parabolic SPDEs Driven by Poisson Random Measure

Maximal regularity for stochastic convolutions driven by Lévy processes

“…the proof of Proposition 3.3 in [17], Theorem 3.1 in [4] for the case q < p, or Corollary C.2 in Appendix C, that for any q ∈ [1, p] there exists a constant C = C q (E) such that for each process ξ as above and for all t ≥ 0,…”

“…We will prove in Appendix C, see also [17] for a different approach to this question, that there exists a unique continuous linear operator which associates with each progressively measurable process ξ :…”

Strong solutions for the stochastic 3D LANS-α model driven by non-Gaussian Lévy noise

“…For the stochastic integral, using the result in ( [26], Corollary 3.1, Remark 3.6 or [40], Lemma 3.1), we have the estimate…”

“…But we need to estimate the fourth order moment of the stochastic integral with respect to the compensated Poisson measure. This is achieved by using the result in ( [26], Corollary 3.1, Remark 3.6 or [40], Lemma 3.1) concerning the maximal inequality for stochastic integral with respect to the compensated Poisson measure. By (9) , (10), as u ∈ L 4 (Ω; L 2 (0, T ; D(A))) and is F t -progressively measurable , then…”

Stochastic FitzHugh-Nagumo equations on networks with impulsive noise

“…The definition of stochastic integral with respect to a compensated Poisson measure has been discussed by many authors, see for instance [1,2,3,9,14,15]. Here we limit ourselves to briefly recalling some conditions for the existence of such integrals.…”