MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 63-72 (2005)

On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes

Tin-Lam Toh, Tuan-Seng Chew

Tin-Lam Toh, National Institute of Education, 1, Nanyang Walk, Singapore 637616, Republic of Singapore, e-mail: tltoh@nie.edu.sg

Abstract: The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Ito integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Ito integral, thereby providing a characterization of Henstock-Kurzweil-Ito integrable stochastic processes in terms of their primitive processes.

Keywords: belated differentiation, Henstock-Kurzweil-Ito integral, integrable processes

Classification (MSC2000): 26A39, 60H05

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