Analytical and Computational Investigations of Stochastic Functional Integral Equations: Solution Existence and Euler–Karhunen–Loève Simulation

Manochehr Kazemi, AliReza Yaghoobnia, Behrouz Parsa Moghaddam and Alexandra Galhano ()
Additional contact information
Manochehr Kazemi: Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian P.O. Box 39618-13347, Iran
AliReza Yaghoobnia: Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran
Behrouz Parsa Moghaddam: Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran
Alexandra Galhano: Faculdade de Ciências Naturais, Engenharias e Tecnologias, Universidade Lusófona do Porto, Rua Augusto Rosa 24, 4000-098 Porto, Portugal

Mathematics, 2025, vol. 13, issue 3, 1-19

Abstract: This paper presents a comprehensive investigation into the solution existence of stochastic functional integral equations within real separable Banach spaces, emphasizing the establishment of sufficient conditions. Leveraging advanced mathematical tools including probability measures of noncompactness and Petryshyn’s fixed-point theorem adapted for stochastic processes, a robust analytical framework is developed. Additionally, this paper introduces the Euler–Karhunen–Loève method, which utilizes the Karhunen–Loève expansion to represent stochastic processes, particularly suited for handling continuous-time processes with an infinite number of random variables. By conducting thorough analysis and computational simulations, which also involve implementing the Euler–Karhunen–Loève method, this paper effectively highlights the practical relevance of the proposed methodology. Two specific instances, namely, the Delay Cox–Ingersoll–Ross process and modified Black–Scholes with proportional delay model, are utilized as illustrative examples to underscore the effectiveness of this approach in tackling real-world challenges encountered in the realms of finance and stochastic dynamics.

Keywords: stochastic functional integral equations; solution existence; Banach space; probability measures of noncompactness; Petryshyn’s fixed-point theorem; Karhunen–Loève expansion; Cox–Ingersoll–Ross process; Modified Black–Scholes models; computational simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/3/427/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/3/427/ (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:3:p:427-:d:1578569

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 ().