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Title: A Riemann approach to random variation (English)
Author: Muldowney, Patrick
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 131
Issue: 2
Year: 2006
Pages: 167-188
Summary lang: English
Category: math
Summary: This essay outlines a generalized Riemann approach to the analysis of random variation and illustrates it by a construction of Brownian motion in a new and simple manner. (English)
Keyword: Henstock integral
Keyword: probability
Keyword: Brownian motion
MSC: 28A20
MSC: 60A99
MSC: 60G05
MSC: 60J65
MSC: 62H30
idZBL: Zbl 1112.28002
idMR: MR2242843
DOI: 10.21136/MB.2006.134089
Date available: 2009-09-24T22:25:23Z
Last updated: 2020-07-29
Stable URL:
Reference: [1] Gordon, R.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock.American Mathematical Society, 1994. Zbl 0807.26004, MR 1288751
Reference: [2] Henstock, R., Muldowney, P., Skvortsov, V. A.: Partitioning infinite-dimensional spaces for generalized Riemann integration.(to appear). MR 2268364
Reference: [3] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus.Springer, Berlin, 1988. MR 0917065
Reference: [4] Kolmogorov, A. N.: Foundations of the Theory of Probability, 1933..
Reference: [5] Muldowney, P.: A General Theory of Integration in Function Spaces, Including Wiener and Feynman Integration.Pitman Research Notes in Mathematics no. 153, Harlow, 1987. Zbl 0623.28008, MR 0887535
Reference: [6] Muldowney, P.: Topics in probability using generalised Riemann integration.Math. Proc. R. Ir. Acad. 99(A)1 (1999), 39–50. Zbl 0965.60010, MR 1883062
Reference: [7] Muldowney, P.: The infinite dimensional Henstock integral and problems of Black-Scholes expectation.J. Appl. Anal. 8 (2002), 1–21. Zbl 1042.28012, MR 1921467, 10.1515/JAA.2002.1
Reference: [8] Muldowney, P., Skvortsov, V. A.: Lebesgue integrability implies generalized Riemann integrability in ${\mathbf R}^{[0,1]}$.Real Anal. Exch. 27 (2001/2002), 223–234. MR 1887853


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