In general textbooks of stochastic process,only the equivalency between mean square differentiability of the process and generalized differentiability of the relevant function about a second moment stochastic process is expounded.

In order to study the focusing properties of cosine-squared Gaussian beams(CsSGB) through a lens without aperture,the equation for the axial irradiance distribution of focused CsSGB are derived based on the Collins formula,and the analytical expression of beams waist width is presented using the second-order moment method.

In this paper, we give two definitions of mean square limit of second order moment fuzzy stochastic process, and prove that the two definitions are equivalent, and discuss the properties of mean square limit of second order moment fuzzy stochastic process.