Keywords
- Brownian Motion
- Quadratic Variation
- Standard Function
- Nonstandard Analysis
- Transfer Principle
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Bibliography
Abrahamse, Allan F., Some applications of nonstandard analysis to the theory of stochastic processes, Preprint No. 35, Dept of Mathematics, University of Southern California, February 1973.
Bernstein, A. and Loeb, P.A., A nonstandard integration theory for unbounded functions, Victoria Symposium on nonstandard analysis, edited, A.E. Hurd and P.A. Loeb, Springer-Verlag Lecture Notes in Math., No. 369, 40–49.
Dudley, R.M., Sample functions of the Gaussian process, Annals of Prob., 1(1973), 66–103.
Fernández de la Vega, W., On almost sure convergence of quadratic Brownian variation, Ann. of Prob., (1974), pp. 551–552.
Garsia, A.M., Topics in Almost Everywhere Convergence, Chicago, 1970.
Hanson, D.L. and Wright, F.T., A bound on tail probabilities for quadratic forms in independent random variables, Annals of Math. Stat., 42 (1971), 1079–1083.
Hersh, Reuben, Brownian motion and nonstandard analysis, Tech. Report 277, Dept. of Mathematics, UNM, May 1973.
Ito, K., Stochastic differentials of continuous local quasi-martingales, stability of stochastic dynamical systems, Lecture Notes in Math., Springer, 294 (1972), 1–7.
Ito, K., Stochastic differentials, to appear in Appl. Math. and Optimization.
Kurtz, Thomas G., Inequalities for the law of large numbers, Annals of Math. Stat., 6 (1972), 1874–1883.
Lamperti, John, Probability, W.A. Benjamin, Inc., New York, Amsterdam, 1966.
Loeb, Peter A., Conversion from nonstandard to standard measure spaces and applications in probability theory, preprint.
Loeb, P.A., A nonstandard representation of measurable spaces, Loo and L*oo, Contributions to nonstandard analysis, edited by W.A.J. Luxemburg and A. Robinson, North-Holland, 1972, 65–80.
Loeb, P.A., A nonstandard representation of Borel Measures and σ-finite measures, Victoria Symposium on nonstandard analysis, edited by A.E. Hurd and P.A. Loeb, Springer-Verlag Lecture Notes in Mathematics, No. 369, 144–152.
Luxemburg, W.A.J., Nonstandard analysis. Lectures on A. Robinson's theory of infinitesimals and infinitely large numbers, Pasadena, 1962.
Muller, D.W. Nonstandard proofs of invariance principles in probability theory, Appl. of Model Theory to Algebra, Analysis and Probability, Holt, Rinehart and Winston, 1969.
Robinson, A., Introduction to model theory and to the metamathematics of algebra, Studies in Logic and the Foundations of Mathematics, Amsterdam, 1963.
Robinson, A., Non-Standard Analysis, North-Holland, Amsterdam, 1970.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag
About this paper
Cite this paper
Greenwood, P., Hersh, R. (1975). Stochastic differentials and quasi-standard random variables. In: Pinsky, M.A. (eds) Probabilistic Methods in Differential Equations. Lecture Notes in Mathematics, vol 451. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0068578
Download citation
DOI: https://doi.org/10.1007/BFb0068578
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07153-2
Online ISBN: 978-3-540-37481-7
eBook Packages: Springer Book Archive
