A Banach Space Leap: Contraction Mapping Solutions for Stochastic Delay Systems

Fatin Nabila Abd Latiff (), Dawn A. Stoner, Kah Lun Wang and Kok Bin Wong
Additional contact information
Fatin Nabila Abd Latiff: Centre for Foundation Studies in Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Dawn A. Stoner: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Kah Lun Wang: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia
Kok Bin Wong: Institute of Mathematical Sciences, Faculty of Science, Universiti Malaya, Kuala Lumpur 50603, Malaysia

Mathematics, 2025, vol. 13, issue 18, 1-11

Abstract: We investigate the solvability and stability properties of a class of nonlinear stochastic delay differential equations (SDDEs) driven by Wiener noise and incorporating discrete time delays. The equations are formulated within a Banach space of continuous, adapted sample paths. Under standard Lipschitz and linear growth conditions, we construct a solution operator and prove the existence and uniqueness of strong solutions using a fixed-point argument. Furthermore, we derive exponential mean-square stability via Lyapunov-type techniques and delay-dependent inequalities. This framework provides a unified and flexible approach to SDDE analysis that departs from traditional Hilbert space or semigroup-based methods. We explore a Banach space fixed-point approach to SDDEs with multiplicative noise and discrete delays, providing a novel functional-analytic framework for examining solvability and stability.

Keywords: fixed-point theory; stochastic delay differential equations; banach spaces; stochastic stability; mean-square analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/18/3002/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/18/3002/ (text/html)

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:gam:jmathe:v:13:y:2025:i:18:p:3002-:d:1751331

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().