| Title:
|
On Itô-Kurzweil-Henstock integral and integration-by-part formula (English) |
| Author:
|
Toh, Tin-Lam |
| Author:
|
Chew, Tuan-Seng |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2005 |
| Pages:
|
653-663 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
generalized Riemann approach |
| Keyword:
|
stochastic integral |
| Keyword:
|
integration-by-parts |
| MSC:
|
26A39 |
| MSC:
|
60H05 |
| idZBL:
|
Zbl 1081.26005 |
| idMR:
|
MR2153089 |
| . |
| Date available:
|
2009-09-24T11:26:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128009 |
| . |
| Reference:
|
[1] T. S. Chew, J. Y. Tay and T. L. Toh: The non-uniform Riemann approach to Itô’s integral.Real Anal. Exchange 27 (2001/2002), 495–514. MR 1922665 |
| Reference:
|
[2] R. Henstock: 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] R. Henstock: Lectures on the Theory of Integration.World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[4] R. Henstock: The General Theory of Integration.Oxford Science, , 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[5] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J. 7 (1957), 418–446. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[6] E. J. McShane: Stochastic Calculus and Stochastic Models.Academic Press, New York, 1974. Zbl 0292.60090, MR 0443084 |
| Reference:
|
[7] Z. R. Pop-Stojanović: On McShane’s belated stochastic integral.SIAM J. Appl. Math. 22 (1972), 89–92. MR 0322954, 10.1137/0122010 |
| Reference:
|
[8] P. Protter: A comparison of stochastic integrals.Ann. Probability 7 (1979), 276–289. Zbl 0404.60062, MR 0525054, 10.1214/aop/1176995088 |
| Reference:
|
[9] P. Protter: Stochastic Integration and Differential Equations.Springer, New York, 1990. Zbl 0694.60047, MR 1037262 |
| Reference:
|
[10] T. L. Toh and T. S. Chew: A variational approach to Itô’s integral.Proceedings of SAP’s 98, Taiwan P291-299, World Scientifc, Singapore, 1999. MR 1819215 |
| Reference:
|
[11] T. L. Toh and T. S. Chew: 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:
|
[12] T. L. Toh: The Riemann approach to stochastic integration.PhD. Thesis, National University of Singapore, Singapore, 2001. |
| Reference:
|
[13] J. G. Xu and P. Y. Lee: Stochastic integrals of Itô and Henstock.Real Anal. Exchange 18 (1992/3), 352–366. MR 1228401 |
| . |
