Ontology of Stochastic Differential Equations

Year 2025, Volume: 20 Issue: 1, 41 - 53

Muharrem Tuncay Gençoğlu

https://doi.org/10.55525/tjst.1561165

Abstract

This study provides a comprehensive examination of the mathematical formulations, ontological foundations, and application domains of stochastic differential equations (SDEs). SDEs play a critical role in modeling complex phenomena such as uncertainty and randomness and can be applied across a wide range of fields from financial markets to biological systems. The paper contrasts the mathematical approaches of Itô and Stratonovich calculus, detailing the solution methods and theoretical foundations of SDEs. Additionally, the ontological foundations of SDEs and their applications in various scientific and engineering fields are explored. Emphasis is placed on their use in finance, biology, cryptology, and blockchain technology. The results highlight the significance of SDEs in mathematical modeling and their impact across numerous application areas.

Keywords

Stochastic Differential Equations, Itô Integral, Stratonovich Integral, Mathematical Modeling.

Supporting Institution

TÜBİTAK

Project Number

223N142

Stokastik Diferansiyel Denklemlerin Ontolojisi

Abstract

Bu çalışma, stokastik diferansiyel denklemlerin (SDE’ler) matematiksel formülasyonları, ontolojik temelleri ve uygulama alanlarının kapsamlı bir incelemesini sunmaktadır. SDE’ler, belirsizlik ve rastgelelik gibi karmaşık olguların modellenmesinde kritik bir rol oynar ve finansal piyasalardan biyolojik sistemlere kadar çok çeşitli alanlarda uygulanabilir. Makale, Itô ve Stratonovich hesabının matematiksel yaklaşımlarını karşılaştırarak SDE’lerin çözüm yöntemlerini ve teorik temellerini ayrıntılı olarak açıklamaktadır. Ek olarak, SDE’lerin ontolojik temelleri ve çeşitli bilimsel ve mühendislik alanlarındaki uygulamaları incelenmektedir. Finans, biyoloji, kriptoloji ve blok zinciri teknolojisindeki kullanımlarına özel vurgu yapılmaktadır. Sonuçlar, SDE’lerin matematiksel modellemedeki önemini ve çok sayıda uygulama alanındaki etkilerini vurgulamaktadır.

Keywords

Stokastik Diferansiyel Denklemler, Itô İntegrali, Stratonovich İntegrali, Matematiksel Modelleme.

Project Number

223N142

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