A noise of new type and its generalized functionals

Volume 96 / 2011

Takeyuki Hida Banach Center Publications 96 (2011), 207-214 MSC: 60H40. DOI: 10.4064/bc96-0-13


The purpose of this paper is to introduce a new noise denoted by $P'(u)$. It has the space parameter $u$, being compared with the usual noise depending on the time $t$. We first explain why such a noise arises naturally. Then, we come to the analysis of functionals of this new noise. We shall emphasize the significance of generalized functionals of $P'(u)$, in particular, linear and quadratic.


  • Takeyuki HidaProfessor Emeritus, Nagoya University

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