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Positive generalized Brownian functionals. (English) Zbl 0817.60045

Hida, T. (ed.) et al., White noise analysis: mathematics and applications. Proceedings of a conference, held in Bielefeld, Germany, 9-15 July, 1989. Singapore: World Scientific Publishing. 407-422 (1990).
Summary: The linear form corresponding to every positive generalized Brownian functional is expressed in terms of the integral form by a positive finite measure defined on the space of all real tempered distributions. The renormalizations like \(\colon\exp [c \int \dot B(u)^ 2d \mu] \colon (c < 1/2)\) or \(\colon\exp [\lambda \dot B(t)]:\;(\lambda, t \in \mathbb{R})\) correspond to Gaussian measures which are singular with respect to the original one.
For the entire collection see [Zbl 0812.00015].

MSC:

60G20 Generalized stochastic processes
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