Domain of Exotic Laplacian Constructed by Wiener Integrals of Exponential White Noise Distributions

In this paper we introduce a new domain of an exotic Laplacian consisting of some white noise distribution-valued Wiener integrals based on exponential distributions in a Fock space, and give a construction of a stochastic process as an infinite dimensional Brownian motion generated by the exotic Laplacians. The Brownian motion generated by the Gross Laplacian is extended to the stochastic process generated by the Lévy Laplacian on the domain. Moreover we give a relationship between semigroups generated by the exotic Laplacians and the Lévy Laplacian on the new domain.