| Title:
|
On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes (English) |
| Author:
|
Toh, Tin-Lam |
| Author:
|
Chew, Tuan-Seng |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
63-72 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
belated differentiation |
| Keyword:
|
Henstock-Kurzweil-Itô integral |
| Keyword:
|
integrable processes |
| MSC:
|
26A39 |
| MSC:
|
60H05 |
| idZBL:
|
Zbl 1112.26012 |
| idMR:
|
MR2128359 |
| DOI:
|
10.21136/MB.2005.134223 |
| . |
| Date available:
|
2009-09-24T22:18:03Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134223 |
| . |
| Reference:
|
[1] Chew T. S., Tay, J. Y., Toh, T. L.: The non-uniform Riemann approach to Itô’s integral.Real Anal. Exch. 27 (2001/2002), 495–514. MR 1922665 |
| Reference:
|
[2] Henstock, R.: The efficiency of convergence factors for functions of a continuous real variable.J. London Math. Soc. 30 (1955), 273–286. Zbl 0066.09204, MR 0072968, 10.1112/jlms/s1-30.3.273 |
| Reference:
|
[3] Henstock, R.: Lectures on the Theory of Integration.World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[4] Lee, P. Y.: Lanzhou Lectures on Henstock Integration.World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957 |
| Reference:
|
[5] McShane, E. J.: Stochastic Calculus and Stochastic Models.Academic Press, New York, 1974. Zbl 0292.60090, MR 0443084 |
| Reference:
|
[6] Oksendal, B.: Stochastic Differential Equation: An Introduction with Applications. 4th edition.Springer, 1996. |
| Reference:
|
[7] Pop-Stojanovic, Z. R.: On McShane’s belated stochastic integral.SIAM J. Appl. Math. 22 (1972), 89–92. Zbl 0243.60035, MR 0322954, 10.1137/0122010 |
| Reference:
|
[8] Toh, T. L., Chew, T. S.: A variational approach to Itô’s integral.Proceedings of SAP’s 98, Taiwan, World Scientific, Singapore, 1999, pp. 291–299. MR 1819215 |
| Reference:
|
[9] Toh, T. L., Chew, T. S.: The Riemann approach to stochastic integration using non-uniform meshes.J. Math. Anal. Appl. 280 (2003), 133–147. MR 1972197, 10.1016/S0022-247X(03)00059-3 |
| Reference:
|
[10] Xu, J. G., Lee, P. Y.: Stochastic integrals of Itô and Henstock.Real Anal. Exch. 18 (1992/3), 352–366. MR 1228401 |
| . |
