| 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:
|
http://hdl.handle.net/10338.dmlcz/134089 |
| . |
| 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 |
| . |
