Weak Second-Order Conditions of Runge–Kutta Method for Stochastic Optimal Control Problems

YILMAZ F. N., Öz Bakan H., Weber G.

Journal of Optimization Theory and Applications, cilt.202, sa.1, ss.497-517, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 202 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s10957-023-02324-y
  • Dergi Adı: Journal of Optimization Theory and Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, ABI/INFORM, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Computer & Applied Sciences, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.497-517
  • Anahtar Kelimeler: 37A50, 49J53, 49K99, 62P05, Optimal control, Runge–Kutta method, Stochastic differential equations, Weak order Taylor expansion
  • Gazi Üniversitesi Adresli: Evet

Özet

In this work, we obtain weak order-2 conditions of Runge–Kutta method for the optimal control of stochastic differential equations which occurs in many areas of economics and finance and recently in cognitive sciences and neuroscience. We get the order conditions that a stochastic Runge–Kutta technique must meet to have weak order two by comparing the stochastic expansion of the approximation with the associated Taylor scheme. Moreover, we present numerical examples which verify the theoretical results. We conclude our paper by a summary and an outlook to future research and application.