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Start Over Creator Toh, Tin-Lam

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

Creator:
Toh, Tin-Lam and Chew, Tuan-Seng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
belated differentiation, Henstock-Kurzweil-Itô integral, and integrable processes
Language:
English
Description:
The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô 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-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô integrable stochastic processes in terms of their primitive processes.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The Kurzweil-Henstock theory of stochastic integration

Creator:
Toh, Tin-Lam and Chew, Tuan-Seng
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
stochastic integral, Kurzweil-Henstock, and convergence theorem
Language:
English
Description:
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. We derive Henstock's Lemmas, absolute continuity property of the primitive process, integrability of stochastic processes and convergence theorems for the Kurzweil-Henstock stochastic integrals. These properties are well-known in the classical (non-stochastic) integration theory but have not been explicitly derived in the classical stochastic integration.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public