Mathematica Bohemica, Vol. 141, No. 2, pp. 129-142, 2016
On Henstock-Kurzweil method to Stratonovich integral
Haifeng Yang, Tin Lam Toh
Abstract: We use the general Riemann approach to define the Stratonovich integral with respect to Brownian motion. Our new definition of Stratonovich integral encompass the classical Stratonovich integral and more importantly, satisfies the ideal Itô formula without the "tail" term, that is, $$f(W_t)= f(W_0)+\int_0^tf'(W_s)\circ dW_s.$$ Further, the condition on the integrands in this paper is weaker than the classical one.
Keywords: Itô formula; Henstock-Kurzweil approach; Stratonovich integral
Affiliations: Haifeng Yang, Tin Lam Toh, National Institute of Education, Nanyang Technological University (NIE/NTU), 1 Nanyang Walk, 637616 Singapore, Republic of Singapore, e-mail: haifeng.yang@nie.edu.sg, tinlam.toh@nie.edu.sg
