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Keywords:
Henstock integral; probability; Brownian motion
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.
References:
[1] Gordon, R.: The Integrals of Lebesgue, Denjoy, Perron, and Henstock. American Mathematical Society, 1994. MR 1288751 | Zbl 0807.26004
[2] Henstock, R., Muldowney, P., Skvortsov, V. A.: Partitioning infinite-dimensional spaces for generalized Riemann integration. (to appear). MR 2268364
[3] Karatzas, I., Shreve, S. E.: Brownian Motion and Stochastic Calculus. Springer, Berlin, 1988. MR 0917065
[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 0887535 | Zbl 0623.28008
[6] Muldowney, P.: Topics in probability using generalised Riemann integration. Math. Proc. R. Ir. Acad. 99(A)1 (1999), 39–50. MR 1883062 | Zbl 0965.60010
[7] Muldowney, P.: The infinite dimensional Henstock integral and problems of Black-Scholes expectation. J. Appl. Anal. 8 (2002), 1–21. DOI 10.1515/JAA.2002.1 | MR 1921467 | Zbl 1042.28012
[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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