|
A nonstandard representation for Brownian motion and Itô integration
Author(s):
Robert M.
Anderson
Journal:
Bull. Amer. Math. Soc.
82
(1976),
99-101.
MSC (1970):
Primary 60H05, 60J65, 02H25
MathSciNet review:
0405581
Retrieve article in:
PDF
References |
Similar articles |
Additional information
References:
- 1.
- Allen R. Bernstein and Frank Wattenberg, Nonstandard measure theory, Applications of Model Theory to Algebra, Analysis, and Probability (Internat. Sympos. Pasadena, Calif., 1967), Holt, Rinehart, and Winston, New York, 1969, pp. 171-185. MR 40 #287. MR 247018
- 2.
- Patrick Billingsley, Convergence of probability measures, John Wiley, New York, 1968. MR 38 #1718. MR 233396
- 3.
- J. L. Doob, Stochastic processes, Wiley, New York; Chapman & Hall, London, 1953. MR 15, 445. MR 58896
- 4.
- Reuben Hersh, Brownian motion and nonstandard analysis, The University of New Mexico Technical Report 277, 1973.
- 5.
- Reuben Hersh and P. Greenwood, Stochastic differentials and quasi-standard random variables (preprint). MR 415766
- 6.
- Kiyosi Itô, On a formula concerning stochastic differentials, Nagoya Math. J. 3 (1951), 55-65. MR 13, 363. MR 44063
- 7.
- Kiyosi Itô, Stochastic integral, Proc. Imp. Acad. Tokyo 20 (1944), 519-542. MR 7, 313. MR 14633
- 8.
- S. Kakutani, Brownian motion and stochastic processes (unpublished lecture notes)
- 9.
- Peter A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Trans. Amer. Math. Soc. 211 (1975), 113-122. MR 390154
- 10.
- H. P. McKean, Jr., Stochastic integrals, Probability and Math. Statist., no. 5, Academic Press, New York, 1969. MR 40 #947. MR 247684
Similar Articles:
Retrieve articles in Bulletin of the American Mathematical Society
with MSC
(1970):
60H05, 60J65, 02H25
Retrieve articles in all Journals with MSC
(1970):
60H05, 60J65, 02H25
Additional Information:
DOI:
10.1090/S0002-9904-1976-13976-6
PII:
S 0002-9904(1976)13976-6
|
