With the aids of a series of mathematical transformations and special functions of mathematical physics, the transition probability density on a sort of systems described by stochastic diffusion process is obtained.

In this paper we study a stochastic differential equation whose solution is a special diffusion with discontinuous coefficient of drift.

For the diffusion on noncompact manifolds,algebraic convergence in L~2-sense is studied.

The paper proposes a new method to estimate nonlinear diffusions based on discretely observed data, and gives some properties of the corresponding parameters estimation.

Random analysis of the continuous sole strong solution of the random diffusion process of a class of the random signals with conditions;

Parameter estimation about the drift coefficient of a diffusion process;

Common framework of single factor interest rate models with diffusion process;

In the paper We discuss opitimal stopping of diffusion processes,because we deal with diffusion processes in the American option pricing.

The small perturbations of one dimensional degenerate diffusion processes is considered.

This article discusses the functional structure of a nonstationary random process on the complete probability space with martingale theory and stochastic analysis process, and ob-tains Wiener processes, diffusion processes, Ito processes and a series of important results ofthe functional structure under Gauss Conditions.