Stochastic evolution equations with Lévy noise in the dual of a nuclear space

被引：0
作者：
C. A. Fonseca-Mora
机构：
[1] Universidad de Costa Rica,Escuela de Matemática
来源：
Stochastics and Partial Differential Equations: Analysis and Computations | 2024年 / 12卷
关键词：
Lévy processes; Dual of a nuclear space; Stochastic integrals; Stochastic evolution equations; Weak convergence; 60H15; 60H05; 60G17; 60B12;
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学科分类号：
摘要：
In this article we give sufficient and necessary conditions for the existence of a weak and mild solution to stochastic evolution equations with (general) Lévy noise taking values in the dual of a nuclear space. As part of our approach we develop a theory of stochastic integration with respect to a Lévy process taking values in the dual of a nuclear space. We also derive further properties of the solution such as the existence of a solution with square moments, the Markov property and path regularity of the solution. In the final part of the paper we give sufficient conditions for the weak convergence of the solutions to a sequence of stochastic evolution equations with Lévy noises.
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页码：173 / 219
页数：46
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