ON L^{p} -ESTIMATES OF MILD SOLUTIONS FOR A CLASS OF SEMILINEAR STOCHASTIC EVOLUTIONS EQUATIONS DRIVEN BY L\'{E}VY AND STABLE PROCESSES - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

ON L^{p} -ESTIMATES OF MILD SOLUTIONS FOR A CLASS OF SEMILINEAR STOCHASTIC EVOLUTIONS EQUATIONS DRIVEN BY L\'{E}VY AND STABLE PROCESSES

Résumé

We study existence and uniqueness of L^{p} ([0, T] \times \Omega)-bounded mild solutions for a class of semilinear stochastic evolutions equations driven by a general class of Lévy processes without Gaussian component including both the non square integrable (\alpha-stable process) and the square integrable cases on a probability space. This is done using a stochastic analysis on the jumps of the L\'evy process pocess with particular attention to the non square inte-grable case (for instance the α-stable process, \alpha ∈ (0, 2)) through a truncation method by separating the big and small jumps together with a classical fixed point theorem ; under local Lipschitz, Hölder, linear growth conditions on the coefficients. Finally, we give an example to show usefulness of the theoritical results that we obtain in this paper.
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Dates et versions

hal-02487388 , version 1 (21-02-2020)

Identifiants

  • HAL Id : hal-02487388 , version 1

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Solym Manou-Abi. ON L^{p} -ESTIMATES OF MILD SOLUTIONS FOR A CLASS OF SEMILINEAR STOCHASTIC EVOLUTIONS EQUATIONS DRIVEN BY L\'{E}VY AND STABLE PROCESSES. 2020. ⟨hal-02487388⟩
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