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Nonstandard Brownian motion in the plane. (English) Zbl 0615.03050

The author restates various results that have apparently appeared in two of his previous papers. Formal proofs do not seem to appear in this article. After a very brief introduction to some of the concepts used in nonstandard analysis, the author then states various known results relative to hyperfinite Loeb measure. These results are then applied to an extended version of Anderson’s original nonstandard construction that leads to a Brownian motion, to harmonic measures and \(C^ 2\) image of Brownian motion.
I point out one misstatement. The set \({\mathcal O}\) of finite numbers is a subring of the nonstandard reals *R and not a subfield as stated.
Reviewer: R.A.Herrmann

MSC:

03H10 Other applications of nonstandard models (economics, physics, etc.)
28A99 Classical measure theory
82B31 Stochastic methods applied to problems in equilibrium statistical mechanics
31A99 Two-dimensional potential theory
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