Structural properties of semilinear SPDEs driven by cylindrical stable processes

By Enrico Priola, Jerzy Zabczyk. 2008

157 citations recorded by the source corpus.

We consider a class of semilinear stochastic evolution equations driven by an additive cylindrical stable noise. We investigate structural properties of the solutions like Markov, irreducibility, stochastic continuity, Feller and strong Feller properties, and study integrability of trajectories. The obtained results are applied to semilinear stochastic heat equations with Dirichlet boundary conditions and bounded and Lipschitz nonlinearities.

Subfields: Control and Systems Engineering, Finance, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/e087de314dfc6f59295033df6cd9ed0d93cc733d

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In Control and Systems Engineering

In Finance

In Modeling and Simulation

Citations in the corpus

Cylindrical Lévy processes in Banach spaces (2009, methodology): “In the monograph [8] by Peszat and Zabczyk an impulsive cylindrical process on L2(O,B(O), λ) is introduced in the following way: let π be the Poisson random measure on [0,∞)×O×Rwith intensity measure ds λ(dξ) ρ(dβ).”
Bismut formula for Lions derivative of distribution-path dependent SDEs (2020, methodology): “Due to their wide applications, the Bismut type formulas have been investigated for different models; see, for instance, [10, 25, 31, 32, 39, 41] for SDEs/SPDEs driven by jump processes, [16, 17, 24, 36, 35, 38, 40] for hypoelliptic diffusion semigroups, and [2, 14, 15] for SDEs with fractional nois”