Generalized convergence characterizations of Feller operator

Abstract

This paper is mainly connected with the generalization of approximation properties of Feller operator. We first introduce the probabilistic properties of the Feller operator and its convergence characterization. We also compute its rates of convergence by means of modulus continuity and moments of random variable Xn. The main theorem is the extension to f (m) derivatives of function f ?CB(m) [0,?). Finally, we are interested in convergence characterization of Laplace transform via Feller operator. © 2011 Pakistan Journal of Statistics.