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A Riemann approach to random variation
Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 167-188
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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.
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.
DOI : 10.21136/MB.2006.134089
Classification : 28A20, 60A99, 60G05, 60J65, 62H30
Keywords: Henstock integral; probability; Brownian motion 
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Muldowney, Patrick. A Riemann approach to random variation. Mathematica Bohemica, Tome 131 (2006) no. 2, pp. 167-188. doi: 10.21136/MB.2006.134089

[1] Gordon, R.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. American Mathematical Society, 1994. | MR | Zbl

[2] Henstock, R., Muldowney, P., Skvortsov, V. A.: Partitioning infinite-dimensional spaces for generalized Riemann integration. (to appear). | MR

[3] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus. Springer, Berlin, 1988. | MR

[4] Kolmogorov, A. N.: Foundations of the Theory of Probability, 1933.

[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. | MR | Zbl

[6] Muldowney, P.: Topics in probability using generalised Riemann integration. Math. Proc. R. Ir. Acad. 99(A)1 (1999), 39–50. | MR | Zbl

[7] Muldowney, P.: The infinite dimensional Henstock integral and problems of Black-Scholes expectation. J. Appl. Anal. 8 (2002), 1–21. | DOI | MR | Zbl

[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

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