Geodesic
On Itô-Kurzweil-Henstock integral and integration-by-part formula
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 653-663
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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.
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.
Classification : 26A39, 60H05
Keywords: generalized Riemann approach; stochastic integral; integration-by-parts 
@article{CMJ_2005_55_3_a6,
     author = {Toh, Tin-Lam and Chew, Tuan-Seng},
     title = {On {It\^o-Kurzweil-Henstock} integral and integration-by-part formula},
     journal = {Czechoslovak Mathematical Journal},
     pages = {653--663},
     year = {2005},
     volume = {55},
     number = {3},
     mrnumber = {2153089},
     zbl = {1081.26005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a6/}
}
TY  - JOUR
AU  - Toh, Tin-Lam
AU  - Chew, Tuan-Seng
TI  - On Itô-Kurzweil-Henstock integral and integration-by-part formula
JO  - Czechoslovak Mathematical Journal
PY  - 2005
SP  - 653
EP  - 663
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a6/
LA  - en
ID  - CMJ_2005_55_3_a6
ER  - 
%0 Journal Article
%A Toh, Tin-Lam
%A Chew, Tuan-Seng
%T On Itô-Kurzweil-Henstock integral and integration-by-part formula
%J Czechoslovak Mathematical Journal
%D 2005
%P 653-663
%V 55
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a6/
%G en
%F CMJ_2005_55_3_a6
Toh, Tin-Lam; Chew, Tuan-Seng. On Itô-Kurzweil-Henstock integral and integration-by-part formula. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 3, pp. 653-663. http://geodesic.mathdoc.fr/item/CMJ_2005_55_3_a6/

[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

[2] R.  Henstock: The efficiency of convergence factors for functions of a continuous real variable. J.  London Math. Soc. 30 (1955), 273–286. | DOI | MR | Zbl

[3] R.  Henstock: Lectures on the Theory of Integration. World Scientific, Singapore, 1988. | MR | Zbl

[4] R.  Henstock: The General Theory of Integration. Oxford Science, , 1991. | MR | Zbl

[5] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (1957), 418–446. | MR | Zbl

[6] E. J.  McShane: Stochastic Calculus and Stochastic Models. Academic Press, New York, 1974. | MR | Zbl

[7] Z. R.  Pop-Stojanović: On McShane’s belated stochastic integral. SIAM J.  Appl. Math. 22 (1972), 89–92. | DOI | MR

[8] P.  Protter: A comparison of stochastic integrals. Ann. Probability 7 (1979), 276–289. | DOI | MR | Zbl

[9] P.  Protter: Stochastic Integration and Differential Equations. Springer, New York, 1990. | MR | Zbl

[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

[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. | DOI | MR

[12] T. L.  Toh: The Riemann approach to stochastic integration. PhD. Thesis, National University of Singapore, Singapore, 2001.

[13] J. G.  Xu and P. Y. Lee: Stochastic integrals of Itô and Henstock. Real Anal. Exchange 18 (1992/3), 352–366. | MR