ABSTRACT
In order to develop stochastic models for the processes of carcinogenesis, this chapter aims to develop some useful mathematical tools and present some stochastic processes which are useful in modeling processes of carcinogenesis. It shows how to solve some first order partial differential equations and a linear Ricatti equation. To describe the stochastic growth of stem cells, intermediate cells and tumor cells, the chapter discusses three important stochastic birth-death processes-the nonhomogeneous Poisson processes, the non-homogeneous Feller-Arley birth-death processes and the stochastic logistic birth-death processes. It presents a brief introduction to the incidence function and the probability generating function of the number of tumors; provides some results which are useful in developing stochastic models of carcinogenesis. In modeling processes of carcinogenesis, an important summary quantity is the age-specific incidence function. To develop stochastic models of carcinogenesis, it is essential to model growth of stem cells, intermediate cells as well as cancer tumor cells.
