This chapter analyzes two basic stochastic models: The time-homogeneous Gaussian and the geometric Wiener diffusion of two-dimensional vector processes. Using the theory of stochastic processes and Ito lemma, the probability of distributions of the stochastic state vectors are described by the evolution of their moments (expectation and covariance as functions of time), as these moments satisfy certain systems of ordinary (deterministic) differential equations (ODE). By solving the latter ODE, the explicit solutions for the first-order and second-order moment functions are presented. The forward Kolmogorov equation is used partly to derive the results by alternative methods and partly to gain information on the probability distributions. The general closed form results on the moment evolutions (still unavailable) have many applications in the models of linear dynamics with uncertainty.