zbMATH — the first resource for mathematics

On Itô-Kurzweil-Henstock integral and integration-by-part formula. (English) Zbl 1081.26005
Summary: In this paper we derive the integration-by-parts formula using the generalized Riemann approach to stochastic integrals, which is called the Itô-Kurzweil-Henstock integral.

26A39 Denjoy and Perron integrals, other special integrals
60H05 Stochastic integrals
Full Text: DOI EuDML
[1] T. S. Chew, J. Y. Tay and T. L. Toh: The non-uniform Riemann approach to Ito’s integral. Real Anal. Exchange 27 (2001/2002), 495–514.
[2] R. Henstock: The efficiency of convergence factors for functions of a continuous real variable. J. London Math. Soc. 30 (1955), 273–286. · Zbl 0066.09204 · doi:10.1112/jlms/s1-30.3.273
[3] R. Henstock: Lectures on the Theory of Integration. World Scientific, Singapore, 1988. · Zbl 0668.28001
[4] R. Henstock: The General Theory of Integration. Oxford Science, 1991. · Zbl 0745.26006
[5] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (1957), 418–446. · Zbl 0090.30002
[6] E. J. McShane: Stochastic Calculus and Stochastic Models. Academic Press, New York, 1974. · Zbl 0292.60090
[7] Z. R. Pop-Stojanovic: On McShane’s belated stochastic integral. SIAM J. Appl. Math. 22 (1972), 89–92. · Zbl 0243.60035 · doi:10.1137/0122010
[8] P. Protter: A comparison of stochastic integrals. Ann. Probability 7 (1979), 276–289. · Zbl 0404.60062 · doi:10.1214/aop/1176995088
[9] P. Protter: Stochastic Integration and Differential Equations. Springer, New York, 1990. · Zbl 0694.60047
[10] T. L. Toh and T. S. Chew: A variational approach to Ito’s integral. Proceedings of SAP’s 98, Taiwan P291–299. World Scientifc, Singapore, 1999. · Zbl 0981.60054
[11] T. L. Toh and T. S. Chew: The Riemann approach to stochastic integration using nonuniform meshes. J. Math. Anal. Appl. 280 (2003), 133–147. · Zbl 1022.60055 · doi:10.1016/S0022-247X(03)00059-3
[12] T. L. Toh: The Riemann approach to stochastic integration. PhD. Thesis. National University of Singapore, Singapore, 2001.
[13] J. G. Xu and P. Y. Lee: Stochastic integrals of Ito and Henstock. Real Anal. Exchange 18 (1992/3), 352–366.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.