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An infinitesimal approach to stochastic analysis

Author: H Jerome Keisler
Publisher: Providence, R.I. : American Mathematical Society, ©1984.
Series: Memoirs of the American Mathematical Society, no. 297.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
This monograph uses Robinson's infinitesimal (i.e., nonstandard) analysis to study stochastic integral equations with respect to a Brownian motion. By using a combination of standard and infinitesimal methods, we obtain new results about stochastic integral equations which can be stated in standard terms.
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: H Jerome Keisler
ISBN: 0821822977 9780821822975
OCLC Number: 10300007
Notes: "March 1984."
"Volume 48, number 297 (third of 4 numbers)."
Description: x, 184 pages ; 26 cm.
Contents: Preliminaries --
Hyperfinite stochastic processes --
The continuity theorem --
Brownian motions and stochastic processes --
Existence theorems for stochastic integral equations --
Properties of solutions --
Lifting theorems --
Uniform lifting theorems --
Internal transformations --
Proof of an existence theorem --
Universality theorems.
Series Title: Memoirs of the American Mathematical Society, no. 297.
Responsibility: H. Jerome Keisler.

Abstract:

This monograph uses Robinson's infinitesimal (i.e., nonstandard) analysis to study stochastic integral equations with respect to a Brownian motion. By using a combination of standard and infinitesimal methods, we obtain new results about stochastic integral equations which can be stated in standard terms.

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