Well Posedness and Asymptotic Behavior for Stochastic Reaction-Diffusion Equations with Multiplicative Poisson Noise

By Carlo Marinelli, Michael Röckner. 2009

53 citations recorded by the source corpus.

We establish well-posedness in the mild sense for a class of stochastic semilinear evolution equations with a polynomially growing quasi-monotone nonlinearity and multiplicative Poisson noise. We also study existence and uniqueness of invariant measures for the associated semigroup in the Markovian case. A key role is played by a new maximal inequality for stochastic convolutions in $L_p$ spaces.

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

View Paper: https://www.semanticscholar.org/paper/fb3e5af8e1082a33167edbdf9dae526c8b179b53

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

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

In Control and Systems Engineering

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

In Finance

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

Citations in the corpus

• 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”
• Stochastic Reaction-diffusion Equations Driven by Jump Processes (2010, unknown): “In another recent paper [55] Marinelli and Röckner investigated a certain class of generalized solutions to problems similar to ours.”