Stochastic systems with memory and jumps
Stochastic systems with memory and jumps
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DOI：
10.1016/j.jde.2018.10.052
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发表时间：
2016-03
影响因子：
2.4
通讯作者：
David R. Banos;David R. Banos;F. Cordoni;G. Nunno;G. Nunno;L. D. Persio;E. Røse
中科院分区：
文献类型：
--
作者：
David R. Banos;David R. Banos;F. Cordoni;G. Nunno;G. Nunno;L. D. Persio;E. Røse
具有记忆的随机系统自然地出现在生命科学、经济和金融领域。我们采取随机泛函延迟方程的建模的观点，我们研究这些结构时，驱动噪声承认跳跃。我们的结果涉及强解的存在性和唯一性，矩的估计和微积分的基本工具，如伊藤公式。研究了解对噪声变化的鲁棒性。具体来说，我们考虑了噪声与无限的活动跳跃与充分校正的高斯噪声。这项研究是在两个不同的框架：我们的工作与随机变量在无限维，其中的值被认为是在一个适当的L p型空间或在空间中的càdlàg路径。从建模的角度来看，值空间的选择是至关重要的，因为不同的设置允许处理不同的记忆或延迟模型。我们的技术涉及无限维微积分和随机微积分通过正则化的工具。
Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate L p-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.