Construction of Levi processes on path spaces of Lie groups

Abstract

Given a compact Lie group and a conjugate-invariant Levi process on it, generated by the operator [Formula: see text], we construct the Levi process on the path space of [Formula: see text], associated with the convolution semigroup [Formula: see text] of probability measures, where [Formula: see text] is the distribution of the Levi process on [Formula: see text] generated by [Formula: see text]. The constructed process is obtained as the weak limit of piecewise constant paths, which, as well as proving its existence and properties, provides finite-dimensional approximations of Chernoff type to the integrals with respect to its distribution.