Nonstandard construction of the stochastic integral and applications to stochastic differential equations. II

Authors:
Douglas N. Hoover and Edwin Perkins

Journal:
Trans. Amer. Math. Soc. **275** (1983), 37-58

MSC:
Primary 60H10; Secondary 03H05

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678335-1

Part I:
Trans. Amer. Math. Soc. (1) (1983), 1-36

MathSciNet review:
678335

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Abstract | References | Similar Articles | Additional Information

Abstract: H. J. Keisler has recently used a nonstandard theory of Itô integration (due to R. M. Anderson) to construct solutions of Itô integral equations by solving an associated internal difference equation. In this paper we use the same general approach to find solutions of semimartingale integral equations of the form

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0678335-1

Keywords:
Stochastic differential equations,
semimartingale,
nonstandard analysis

Article copyright:
© Copyright 1983
American Mathematical Society