Sains Malaysiana 46(12)(2017): 2549–2554

http://dx.doi.org/10.17576/jsm-2017-4612-33

 

Transformation and Differentiation of Henstock-Wiener Integrals

(Transformasi dan Pembezaan Kamiran Henstock-Wiener)

 

VARAYU BOONPOGKRONG^1* & ELVIRA PEDERES DE LARA-TUPRIO²

 

¹Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, 90112, Thailand

 

²Mathematics Department, Ateneo de Manila University Loyola Hts., Quezon City, 1108, Philippines

 

Received: 8 November 2016/Accepted: 18 April 2017

 

ABSTRACT

In this paper, transformation and differentiation of Henstock-Wiener integrals are discussed. The approach is by Riemann sums. The idea is more transparent than that of classical Wiener integral.

 

Keywords: Cameron-Martin theorem; Henstock integral; Henstock-Kurzweil integral; Wiener integral

ABSTRAK

Kertas ini membincangkan transformasi dan perbezaan kamiran Henstock-Wiener. Pendekatan yang digunakan ialah congak Riemann. Idea ini lebih telus berbanding klasik integral Wiener.

 

Kata kunci: Cameron-Martin theorem; Henstock integral; Henstock-Kurzweil integral; Wiener integral

REFERENCES

 

Apostol, T.M. 1957. Mathematical Analysis. Boston: Addison-Wesley.

Cabral, E. & Lee, P.Y. 2000-2001. A fundamental theorem of calculus for the Kurzweil-Henstock integrals in xxx. Real Analysis Exchange 26: 867-876.

Cameron, R.H. & Martin, W.T. 1944. Transformations of Wiener integrals under translations. Annals of Mathematics 45(2): 386-396.

Chew, T.S. & Lee, P.Y. 1994. The Henstock-Wiener integral. Proceeding of Symposium on Real Analysis (Xiamen 1993). J. Math. Study 27(1): 60-65.

Henstock, R. 1988. Lectures on the Theory of Integration. Singapore: World Scientific.

Kurzweil, J. 2000. Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces. Singapore: World Scientific.

Lee, P.Y. & Výborný, R. 2000. The Integral: An Easy Approach after Kurzweil and Henstock. Cambridge: Cambridge University Press.

Lu, J. & Lee, P.Y. 1999. The primitive of Henstock integrable functions in Euclidean space. Bull. London Math. Society 31: 173-180.

Muldowney, P. 2012. A Modern Theory of Random Variation With Applications in Stochastic Calculus, Financial Mathematics, and Feynman Integration. New York: John Wiley & Sons.

Muldowney, P. 1987. A General Theory of Integration in Function Spaces, including Wiener and Feynman Integration. Pitman Research Notes in Mathematics Series. Harlow: Longman.

Yang, C.H. 1998. Measure theory and the Henstock-Wiener integral. M.Sc. Thesis. NUS (unpublished).

Yang, C.H. & Chew, T.S. 1999. On McShane-Wiener integral. Proceeding of International Mathematics Conference (Manila 1998), Matimyas Math. 22(2): 39-46.

 

 

*Corresponding author; email: varayu.b@psu.ac.th