A Riemann approach to random variation

Patrick Muldowney

Mathematica Bohemica (2006)

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

Abstract

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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.

How to cite

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Muldowney, 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

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  1. The Integrals of Lebesgue, Denjoy, Perron, and Henstock, American Mathematical Society, 1994. (1994) Zbl0807.26004MR1288751
  2. Partitioning infinite-dimensional spaces for generalized Riemann integration, (to appear). (to appear) MR2268364
  3. Brownian Motion and Stochastic Calculus, Springer, Berlin, 1988. (1988) MR0917065
  4. Foundations of the Theory of Probability, 1933, . 
  5. 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
  6. Topics in probability using generalised Riemann integration, Math. Proc. R. Ir. Acad. 99(A)1 (1999), 39–50. (1999) Zbl0965.60010MR1883062
  7. The infinite dimensional Henstock integral and problems of Black-Scholes expectation, J. Appl. Anal. 8 (2002), 1–21. (2002) Zbl1042.28012MR1921467
  8. Lebesgue integrability implies generalized Riemann integrability in 𝐑 [ 0 , 1 ] , Real Anal. Exch. 27 (2001/2002), 223–234. (2001/2002) MR1887853

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