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

By Erika Hausenblas. 2005

76 citations recorded by the source corpus.

In this paper we investigate SPDEs in certain Banach spaces driven by a Poisson random measure. We show existence and uniqueness of the solution, investigate certain integrability properties and verify the cadlag property.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/90a0534fd204ae02ba948db767e87661e150698f

How researchers see this paper

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In Computational Theory and Mathematics

1. Zdzisław Brzeźniak
2. Wei David Liu
3. Jiahui Zhu
4. Erika Hausenblas
5. Arnulf Jentzen
6. Bixiang Wang
7. Peter E. Kloeden
8. Yubin Yan

In Control and Systems Engineering

1. Zdzisław Brzeźniak
2. Wei David Liu
3. Jiahui Zhu
4. Erika Hausenblas
5. El.zbieta Motyl
6. Michael Röckner
7. Bixiang Wang
8. Wei Liu

In Finance

1. Zdzisław Brzeźniak
2. Wei David Liu
3. Jiahui Zhu
4. Erika Hausenblas
5. El.zbieta Motyl
6. J. V. Neerven
7. Michael Röckner
8. Bixiang Wang

Citations in the corpus

• Stochastic Convolutions Driven by Martingales: Maximal Inequalities and Exponential Integrability (2007, unknown): “, [1, 2, 16, 21, 25, 36] and the references therein).”
• Strong solutions for SPDE with locally monotone coefficients driven by L\'{e}vy noise (2011, background): “tensively investigated by many authors, see e.g. Kallianpur and Xiong [24], Albeverio et al [2], Mueller et al [40, 41], Applebaum and Wu [3], Mytnik [42], Truman and Wu [53], Knoche [25], Hausenblas [22, 23], ∗Corresponding author: wei.liu@uni-bielefeld.de 1 Mandrekar and Ru¨diger [36], Ro¨ckner an”
• SPDEs driven by Poisson random measure with non Lipschitz coefficients: existence results (2006, methodology): “As described in [9], Section 5 or Remark 2.”
• Maximal regularity for stochastic convolutions driven by Lévy processes (2009, background): “the proof of Proposition 3.3 in [ 17 ], Theorem 3.1 in [4 ]f or”
• Stochastic Reaction-diffusion Equations Driven by Jump Processes (2010, unknown): “Our paper confirms an observation that has already been made in earlier papers [13, 42] that the theory of stochastic integration with respect to a Poisson random measure in martingale type p Banach spaces is, to a large extend, analogous to the theory of stochastic integration with respect to a cyl”