Some Stochastic Growth Processes

Abstract

The growth of non~saturating and saturating populations is modeled by a general kind of stochastic differential equation. The transition density functions of the solutions of these equations, obtained using the Stratonovich stochastic integral, are obtained in closed form. Moments, first passage time probability densities and probabilities of extinction can be found explicitly in a number of cases. Specifically considered are Malthusian growth, a general non-saturating process, a general saturating process which contains the Pearl-Verhulst model as a special case, and Gompertzian growth. This last-named process is examined with a view to the stochastic modeling of large populations of tumor cells.