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

Tin-Lam Toh; Tuan-Seng Chew

Mathematica Bohemica (2005)

  • Volume: 130, Issue: 1, page 63-72
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Toh, Tin-Lam, and Chew, Tuan-Seng. "On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes." Mathematica Bohemica 130.1 (2005): 63-72. <http://eudml.org/doc/249598>.

@article{Toh2005,
abstract = {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.},
author = {Toh, Tin-Lam, Chew, Tuan-Seng},
journal = {Mathematica Bohemica},
keywords = {belated differentiation; Henstock-Kurzweil-Itô integral; integrable processes; Henstock-Kurzweil-Itô integral},
language = {eng},
number = {1},
pages = {63-72},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes},
url = {http://eudml.org/doc/249598},
volume = {130},
year = {2005},
}

TY - JOUR
AU - Toh, Tin-Lam
AU - Chew, Tuan-Seng
TI - On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes
JO - Mathematica Bohemica
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 130
IS - 1
SP - 63
EP - 72
AB - 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.
LA - eng
KW - belated differentiation; Henstock-Kurzweil-Itô integral; integrable processes; Henstock-Kurzweil-Itô integral
UR - http://eudml.org/doc/249598
ER -

References

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  3. Lectures on the Theory of Integration, World Scientific, Singapore, 1988. (1988) Zbl0668.28001MR0963249
  4. Lanzhou Lectures on Henstock Integration, World Scientific, Singapore, 1989. (1989) Zbl0699.26004MR1050957
  5. Stochastic Calculus and Stochastic Models, Academic Press, New York, 1974. (1974) Zbl0292.60090MR0443084
  6. Stochastic Differential Equation: An Introduction with Applications. 4th edition, Springer, 1996. (1996) 
  7. 10.1137/0122010, SIAM J. Appl. Math. 22 (1972), 89–92. (1972) Zbl0243.60035MR0322954DOI10.1137/0122010
  8. A variational approach to Itô’s integral, Proceedings of SAP’s 98, Taiwan, World Scientific, Singapore, 1999, pp. 291–299. (1999) MR1819215
  9. 10.1016/S0022-247X(03)00059-3, J. Math. Anal. Appl. 280 (2003), 133–147. (2003) MR1972197DOI10.1016/S0022-247X(03)00059-3
  10. Stochastic integrals of Itô and Henstock, Real Anal. Exch. 18 (1992/3), 352–366. (1992/3) MR1228401

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