Stratonovich-Henstock integral for the operator-valued stochastic process

• Canton, Recson ^[1] ; Labendia, Mhelmar ^[1] ; Toh, Tin Lam ^[2]
  1. [1] Mindanao State University

     Mindanao State University

     Marawi City, Filipinas

     
  2. [2] National Institute of Education.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 5, 2022, págs. 1111-1130
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-5018
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we introduce the Stratonovich-Henstock integral of an operator-valued stochastic process with respect to a Q-Wiener process. We also formulate a version of Ito's formula for this integral.

• Referencias bibliográficas
  • J.-P. Aubin, Applied functional analysis: Aubin/applied, 2nd ed. Nashville, TN: John Wiley & Sons, 2011. https://doi.org/10.1002/9781118032725
  • T. S. Chew, T. L. Toh, and J. Y. Tay, “The non-uniform Riemann approach to Itô’s integral,” Real Analysis Exchange, vol. 27, no. 2, pp. 495-514,...
  • G. Da Prato and J. Zabczyk, Encyclopedia of mathematics and its applications volume 44: Stochastic equations in infinite dimensions. Cambridge:...
  • J. Dieudonné, Foundations of modern analysis. San Diego, CA: Academic Press, 1969. https://doi.org/10.1126/science.132.3441.1759-a
  • L. Gawarecki and V. Mandrekar, Stochastic differential equations in infinite dimensions: With applications to stochastic partial differential...
  • R. A. Gordon, The integrals of Lebesgue, Denjoy, Perron and Henstock. Providence, RI: American Mathematical Society, 1994. https://doi.org/10.1090/gsm/004
  • R. Henstock, Lectures on the theory of integration. Singapore: World Scientific Publishing, 1988. https://doi.org/10.1142/0510
  • J. Kurzweil, Henstock-Kurzweil integration: Its relation to topological vector spaces. Singapore, Singapore: World Scientific Publishing,...
  • J. Kurzweil and S. Schwabik, “McShane equi-integrability and Vitali’s convergence theorem”, Mathematica Bohemica, vol. 129, no. 2, pp. 141-157,...
  • M. Labendia and J. Arcede, “A descriptive definition of the Itô-Henstock integral for the operator-valued stochastic process”, Advances in...
  • M. Labendia, T. R. Teng, and E. De Lara-Tuprio, “Itô-Henstock integral and Itô’s formula for the operator-valued stochastic process”, Mathematica...
  • P. Y. Lee, Lanzhou lectures on Henstock integration. Singapore: World Scientific Publishing, 1989. https://doi.org/10.1142/0845
  • P. Y. Lee and R. Výborný, The Integral: An Easy Approach after Kurzwiel and Henstock. Australian mathematical society lecture series 14. Cambridge:...
  • T. Y. Lee, Henstock-Kurzweil integration on euclidean spaces. Singapore: World Scientific Publishing, 2011. https://doi.org/10.1142/7933
  • J. T. Lu and P. Y. Lee, “The primitives of Henstock integrable functions in Euclidean space”, Bulletin of the London Mathematical Society,...
  • Z. M. Ma, Z. Grande, and P. Y. Lee, “Absolute integration using Vitali covers”, Real Analysis Exchange, vol. 18, no. 2, pp. 409-419, 1992....
  • E. J. McShane, “Stochastic integrals and stochastic functional equations”, SIAM Journal on Applied Mathematics, vol. 17, no. 2, pp. 287-306,...
  • Z. R. Pop-Stojanovic, “On McShane’s belated stochastic integral”, SIAM Journal on Applied Mathematics, vol. 22, no. 1, pp. 87-92, 1972. https://doi.org/10.1137/0122010
  • C. Prévót and M. Röckner, A concise course on stochastic partial differential equations. Berlin: Springer, 2007. https://doi.org/10.1007/978-3-540-70781-3
  • M. Reed and B. Simon, Methods of modern mathematical physics: Functional analysis, v. 1. San Diego, CA: Academic Press, 1972. https://doi.org/10.1016/B978-0-12-585001-8.X5001-6
  • R. Rulete and M. Labendia, “Backwards Itô-Henstock integral for the Hilbert-Schmidt-valued stochastic process”, European Journal of Pure and...
  • R. Rulete and M. Labendia, “Backwards Itô-Henstock’s version of Itô’s formula”, Annals of Functional Analysis, vol. 11, no. 1, pp. 208-225,...
  • C. W. Swartz, Introduction to gauge integrals. Singapore: World Scientific Publishing, 2001. https://doi.org/10.1142/4361
  • T. L. Toh and T. S. Chew, “On belated differentiation and a characterization of Henstock-Kurzweil-Itô integrable processes”, Mathematica Bohemica,...
  • T. L. Toh and T. S. Chew, “On Itô-Kurzweil-Henstock integral and integration-by-part formula”, Czechoslovak Mathematical Journal, vol. 55,...
  • T. L. Toh and T. S. Chew, “On the Henstock-Fubini theorem for multiple stochastic integrals”, Real Analysis Exchange, vol. 30, no. 1, pp....
  • T. L. Toh and T. S. Chew, “The Riemann approach to stochas tic integration using non-uniform meshes”, Journal of Mathematical Analysis and...
  • H. Yang and T. L. Toh, “On Henstock-Kurzweil method to Stratonovich integral”, Mathematica Bohemica, vol. 141, no. 2, pp. 129-142. https://doi.org/10.21136/MB.2016.11