caa a22 4500 475839285 CHVBK 20180406123857.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1023/A:1010779905082 doi (NATIONALLICENCE)springer-10.1023/A:1010779905082 Potthoff Jürgen Lehrstuhl für Mathematik V, Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany aut On Differential Operators in White Noise Analysis [Elektronische Daten] [Jürgen Potthoff] 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. Kluwer Academic Publishers, 2000 white noise analysis nationallicence Malliavin calculus nationallicence differential operators nationallicence Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 333-347 0167-8019 63:1-3<333 2000 63 10440 https://doi.org/10.1023/A:1010779905082 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1010779905082 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Potthoff Jürgen Lehrstuhl für Mathematik V, Fakultät für Mathematik und Informatik, Universität Mannheim, D-68131, Mannheim, Germany aut NATIONALLICENCE 773 0- Acta Applicandae Mathematica Kluwer Academic Publishers 63/1-3(2000-09-01), 333-347 0167-8019 63:1-3<333 2000 63 10440 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer