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On the regularity of stochastic difference equations in hyperfinite-dimensional vector spaces and applications to -valued stochastic differential equations
Published online by Cambridge University Press: 14 November 2011
Abstract
Nonstandard analysis is used, in this paper, to give a construction of a Wiener -process Wt, t ∈ [0, ∞). From this, a hyperfinite representation of stochastic integrals for operatorvalued processes with respect to Wt is derived, and existence theorems in the spirit of Keisler are proved for (infinite-dimensional) stochastic differential equations of Itô's type one and a certain kind of Itô's type two, via regularity of hyperfinite stochastic difference equations.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 6 , 1994 , pp. 1089 - 1117
- Copyright
- Copyright © Royal Society of Edinburgh 1994
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