Stability in distribution for stochastic differential equations with memory driven by positive semigroups and Lévy processes

Kai Liu

Applied Mathematics and Computation, 2019, vol. 362, issue C, -

Abstract: In this paper, we consider stationarity of a class of stochastic differential equations with memory driven by Lévy processes in Banach spaces. The stochastic systems under investigation have linear operators acting on point or distributed delayed terms and the operators acting on the instantaneous term generate positive strongly continuous semigroups. The asymptotic behavior of the associated deterministic systems is considered through the useful Weis Theorem on a Banach lattice, and the stationarity of the generalized nonlinear stochastic systems is established through a weak convergence programme. Last, our theory is illustrated by its application to a stochastic age-structured population model with memory on which the usual spectral-determined growth condition type of scheme seems to be impossibly carried out.

Keywords: Stationary solution; Positive semigroup; Lévy process; Stochastic differential equation with memory (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300319305727
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:362:y:2019:i:c:2

DOI: 10.1016/j.amc.2019.124580

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().