On Henstock-Kurzweil method to Stratonovich integral. (English) Zbl 1389.26016

Yang, Haifeng; Toh, Tin Lam

Math. Bohem. 141, No. 2, 129-142 (2016).

Summary: 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, \[ f(W_t)=f(W_0)+\int_0^tf'(W_s)\circ\text{d}W_s. \] Further, the condition on the integrands in this paper is weaker than the classical one.

MSC:

26A39	Denjoy and Perron integrals, other special integrals
60H05	Stochastic integrals

Keywords:

Itô formula; Henstock-Kurzweil approach; Stratonovich integral