Generalized Riccati Wick differential equation and applications

Using the Wick derivation operator and the Wick product of elements in a distribution space Fθ∗(SC′)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {F}}_\theta ^*({\mathcal {S}}'_{{\mathbb {C}}})$$\end{document}, we introduce the generalized Riccati Wick differential equation as a distribution analogue of the classical Riccati differential equation. The solution of this new equation is given. Finally, we finish this paper by building some applications.