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

Tin-Lam Toh; Tuan-Seng Chew

Displaying similar documents to “On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes”

The Kurzweil-Henstock theory of stochastic integration

Tin-Lam Toh, Tuan-Seng Chew (2012)

Czechoslovak Mathematical Journal

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The Kurzweil-Henstock approach has been successful in giving an alternative definition to the classical Itô integral, and a simpler and more direct proof of the Itô Formula. The main advantage of this approach lies in its explicitness in defining the integral, thereby reducing the technicalities of the classical stochastic calculus. In this note, we give a unified theory of stochastic integration using the Kurzweil-Henstock approach, using the more general martingale as the integrator....

On Itô-Kurzweil-Henstock integral and integration-by-part formula

Tin-Lam Toh, Tuan-Seng Chew (2005)

Czechoslovak Mathematical Journal

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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.

Itô-Henstock integral and Itô's formula for the operator-valued stochastic process

Mhelmar A. Labendia, Timothy Robin Y. Teng, Elvira P. de Lara-Tuprio (2018)

Mathematica Bohemica

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In this paper, we introduce the Itô-Henstock integral of an operator-valued stochastic process and formulate a version of Itô's formula.

Banach-valued Henstock-Kurzweil integrable functions are McShane integrable on a portion

Tuo-Yeong Lee (2005)

Mathematica Bohemica

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It is shown that a Banach-valued Henstock-Kurzweil integrable function on an $m$ -dimensional compact interval is McShane integrable on a portion of the interval. As a consequence, there exist a non-Perron integrable function $f {[0, 1]}^{2} ⟶ ℝ$ and a continuous function $F {[0, 1]}^{2} ⟶ ℝ$ such that $(¶) \int_{0}^{x} \{(¶) \int_{0}^{y} f (u, v) d v\} d u = (¶) \int_{0}^{y} \{(¶) \int_{0}^{x} f (u, v) d u\} d v = F (x, y)$ for all $(x, y) \in {[0, 1]}^{2}$ .