An \(L_p\)-theory for stochastic partial differential equations driven by Lévy processes with pseudo-differential operators of arbitrary order

DOI10.1016/j.spa.2016.03.001zbMath1344.60062OpenAlexW2296583183MaRDI QIDQ737179

Kyeong-Hun Kim, Ildoo Kim

Publication date: 8 August 2016

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2016.03.001

zbMATH Keywords

Lévy processesstochastic partial differential equationspseudo-differential operators\(L_p\)-theory

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Pseudodifferential operators (47G30) Initial value problems for PDEs with pseudodifferential operators (35S10)

Related Items (8)

An \(L_p\)-maximal regularity estimate of moments of solutions to second-order stochastic partial differential equations ⋮ Schauder estimates for stochastic transport-diffusion equations with Lévy processes ⋮ A weighted \(L_p\)-regularity theory for parabolic partial differential equations with time-measurable pseudo-differential operators ⋮ BMO and Morrey-Campanato estimates for stochastic convolutions and Schauder estimates for stochastic parabolic equations ⋮ Hölder continuous of the solutions to stochastic nonlocal heat equations ⋮ A Kolmogorov-type theorem for stochastic fields ⋮ A regularity theory for stochastic partial differential equations driven by multiplicative space-time white noise with the random fractional Laplacians ⋮ On the Campanato and Hölder regularity of local and nonlocal stochastic diffusion equations

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