In this paper a diffusion approximation to the two-type Galton-Watson branching processes with mean matrix close to the identity is given in the form of Berstein stochastic differentials. An associated diffusion equation is found using an extension of the one-dimensional Bernstein technique....

Due to the advances in computer technology a lot of industrial, biological, and medical processes are continuously monitored by instruments under the control of microprocessors. Thus, our data is a set of curves defined on certain time intervals, i.e., sample paths of continuous-time stochastic...

In this paper we extend the method of Bernstein using some concepts of differential geometry and prove the existence of a partial differential equation which when solved under suitable boundary conditions leads to a density of a bivariate inverse Gaussian process.