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On Differential Operators in White Noise Analysis

In: Recent Developments in Infinite-Dimensional Analysis and Quantum Probability

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  • Jürgen Potthoff

    (Universität Mannheim, Lehrstuhl für Mathematik V, Fakultät für Mathematik und Informatik)

Abstract

White noise analysis is formulated on a general probability space which is such that (1) it admits a standard Brownian motion, and (2) its σ-algebra is generated by this Brownian motion (up to completion). As a special case, the white noise probability space with time parameter being the half-line is worked out in detail. It is shown that the usual differential operators can be defined on the smooth, finitely based functions of at most exponential growth via the chain rule, without supposing the existence of a linear structure (or translations) on the underlying probability space.

Suggested Citation

  • Jürgen Potthoff, 2001. "On Differential Operators in White Noise Analysis," Springer Books, in: Luigi Accardi & Hui-Hsiung Kuo & Nobuaki Obata & Kimiaki Saito & Si Si & Ludwig Streit (ed.), Recent Developments in Infinite-Dimensional Analysis and Quantum Probability, pages 333-347, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0842-6_24
    DOI: 10.1007/978-94-010-0842-6_24
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