We focus on the stochastic description of the stock price dynamics. Thereby we concentrate on the Heston model and the Hull-White model. We derive the stationary probability density distribution of the variance of both models in the case of zero correlation coefficient. These distributions are used to calculate solutions for the logarithmic returns of the stock price for short time lags. Furthermore we compare the received results with numerical simulations. In addition we apply the solutions of both models to the German tick-by-tick Dax data. The data are from May 1996 to December 2001. We use the probability density distributions of the logarithmic returns, calculated out of the data, and fit these distributions to the theoretical distributions.
We present a comparison of nucleation in an isothermal-isochoric container with traffic congestion on a one-lane freeway. The analysis is based, in both cases, on the probabilistic description by stochastic master equations. Further we analyze the characteristic features of traffic breakdowns. To describe this phenomenon we apply the stochastic model regarding the jam emergence to the formation of a large car cluster on the highway.