ABSTRACT
Under suitable conditions, stochastic mathematical models of dynamic systems described by diffusion processes (probabilistic laws) and systems of stochastic differential equations of Itô-type (Newtonian type laws) are equivalent. The concept of system of stochastic differential equations of Itô-type generates a very natural and straightforward but a difficult problem of “stochastic versus deterministic.” In this case, this means that to what extent the solution processes of systems of stochastic differential equations of Itôtype deviate from the solution processes of corresponding systems of deterministic differential equations that are described by drift coefficient vector functions of the corresponding diffusion processes as rate functions. Furthermore, “stochastic versus deterministic” problem can be studied by studying the characterization of the diffusion coefficient square matrix functions of the corresponding diffusion processes. This is because of the fact that the diffusion coefficient matrix function of the diffusion process is a measure of the local magnitude of the random fluctuations of the diffusion process.
