Abstract
The main objective of this paper is to investigate an extension Delta(ext)(G)(K) of the "Volterra-Gross" Laplacian on nuclear algebra of generalized functions. In so doing, without using the renormalization procedure, this extension provides a continuous nuclear realization of the square white noise Lie algebra obtained by Accardi-Franz-Skeide in Ref. 2. An extended-Gross diffusion process driven by a class of Ito stochastic equations is studied, and solution of the related Poisson equations is derived in terms of a suitable lambda-potential.