Classical and nonclassical Levy Laplacians

A general method for defining and studying operators introduced by Paul Levy referred as classical Levy Laplacians and their modifications referred as nonclassical Laplacians, which makes its possible to extend results on Levy Laplacians to nonclassical Laplacians, has been discussed. An infinite family of Laplacians, whose elements are classical Laplacians and the non-classical Laplacians related to the Yang-Mills equations, has been defined and the relationship between these Laplacians and quantum random process has been described. A quantum random process is a function defined on a part of the real line and taking values in some space of operators. Volterra Laplacians have also been considered and analogies between them and Levy Laplacians have been found.