In this model the stochastic process is a geometric Brownian motion.
This model is based on the Black Scholes Model but with the assumption that the square volatility is a stochastic process itself. The square of volatility is assumed to be a so called Cox-Ingersoll-Ross mean reversion process, i.e. a process which is fluctuating about a mean value. More details about this process and ways to price derivatives with this model can be found on the homepage of Gunter Winkler and in the formula catalogue.
This model is based on the Black Scholes Model with an additional jump process. The time gap between two jumps are exponentially distributed and the hight of each jump is proportional to the current share price and to a lognormal distributed random variable. More details about this process and a discussion of anti trend strategies in this model can be found on the homepage of Dana Uhlig-Düvelmeyer (in German only).