# A Riemann approach to random variation

Mathematica Bohemica (2006)

- Volume: 131, Issue: 2, page 167-188
- ISSN: 0862-7959

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topMuldowney, Patrick. "A Riemann approach to random variation." Mathematica Bohemica 131.2 (2006): 167-188. <http://eudml.org/doc/249903>.

@article{Muldowney2006,

abstract = {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.},

author = {Muldowney, Patrick},

journal = {Mathematica Bohemica},

keywords = {Henstock integral; probability; Brownian motion; Henstock integral; probability; Brownian motion},

language = {eng},

number = {2},

pages = {167-188},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {A Riemann approach to random variation},

url = {http://eudml.org/doc/249903},

volume = {131},

year = {2006},

}

TY - JOUR

AU - Muldowney, Patrick

TI - A Riemann approach to random variation

JO - Mathematica Bohemica

PY - 2006

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 131

IS - 2

SP - 167

EP - 188

AB - 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.

LA - eng

KW - Henstock integral; probability; Brownian motion; Henstock integral; probability; Brownian motion

UR - http://eudml.org/doc/249903

ER -

## References

top- The Integrals of Lebesgue, Denjoy, Perron, and Henstock, American Mathematical Society, 1994. (1994) Zbl0807.26004MR1288751
- Partitioning infinite-dimensional spaces for generalized Riemann integration, (to appear). (to appear) MR2268364
- Brownian Motion and Stochastic Calculus, Springer, Berlin, 1988. (1988) MR0917065
- Foundations of the Theory of Probability, 1933, .
- A General Theory of Integration in Function Spaces, Including Wiener and Feynman Integration, Pitman Research Notes in Mathematics no. 153, Harlow, 1987. (1987) Zbl0623.28008MR0887535
- Topics in probability using generalised Riemann integration, Math. Proc. R. Ir. Acad. 99(A)1 (1999), 39–50. (1999) Zbl0965.60010MR1883062
- The infinite dimensional Henstock integral and problems of Black-Scholes expectation, J. Appl. Anal. 8 (2002), 1–21. (2002) Zbl1042.28012MR1921467
- Lebesgue integrability implies generalized Riemann integrability in ${\mathbf{R}}^{[0,1]}$, Real Anal. Exch. 27 (2001/2002), 223–234. (2001/2002) MR1887853

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