Conditionally Gaussian Random Processes

A class of non-Gaussian processes $(\theta_t,\xi_t,0\leqslant t\leqslant T)$ is defined by means of nonlinear Ito stochastic differential equations with the property that the conditional finite-dimensional distribution functions of the process $(\theta_s,s\leqslant t)$ subject to the condition $(\xi_s,s\leqslant t)$ are with probability 1 Gaussian. This fact yields effective results in statistical problems of random processes, in particular a nonlinear generalization of the Kalman?Bucy filtering problem.