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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2013; 50(3): 607-625

Printed May 1, 2013

https://doi.org/10.4134/JKMS.2013.50.3.607

Copyright © The Korean Mathematical Society.

Reflection principles for general Wiener function spaces

Ian Pierce and David Skoug

St. Olaf College, University of Nebraska-Lincoln

Abstract

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It is well-known that the ordinary single-parameter Wiener space exhibits a reflection principle. In this paper we establish a reflection principle for a generalized one-parameter Wiener space and apply it to the integration of a class of functionals on this space. We also discuss several notions of a reflection principle for the two-parameter Wiener space, and explore whether these actually hold.

Keywords: generalized Wiener space, Yeh-Wiener space, generalized Brownian motion, distribution of supremum

MSC numbers: 28C20, 46G12, 60G20

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