Elements of stochastic analysis for the case of Grassmann variables. III. Correlation functions

The present paper continues earlier studies [1, 2], in which analogs were proposed in the case of Grassmann variables for concepts such as classical stochastic analysis, stochastic integrals, random processes, and stochastic partial differential equations and their solutions. This was done for the special case when the classical objects are functionals of a so-called smoothed Wiener process on ${\mathbf R}_{+} \times {\mathbf R} ^{\nu }$. In the present paper, the correlation functions of the solution of a stochastic partial differential equation are studied together with some applications.