A noise of new type and its generalized functionals
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.