In this article, the risk process perturbed by diffusion under interest force is considered, the continuity and twice continuous differentiability for Фδ（u,w） are discussed,the Feller expression and the integro-differential equation satisfied by Фδ （u ,w） are derived. Finally, the decomposition of Фδ（u,w） is discussed, and some properties of each decomposed part of Фδ（u,w） are obtained. The results can be reduced to some ones in Gerber and Landry＇s,Tsai and Willmot＇s, and Wang＇s works by letting parameter δ and （or） a be zero.
In this paper a class of risk processes in which claims occur as a renewal process is studied. A clear expression for Laplace transform of the survival probability is well given when the claim amount distribution is Erlang distribution or mixed Erlang distribution. The expressions for moments of the time to ruin with the model above are given.
