Analytic Random Processes

This paper is devoted to investigating the so-called analytic random processes. Random process $\xi(t)$ is called analytic in a region $D$ if almost all its sample functions are analytic and possess an analytic continuation in the region $D$. Analyticity of the covariance function $B(t,s)=\mathbf M\xi(t)\xi (s)$ in the neighborhood of $(t_0,t_0)$ is a sufficient condition for analyticity of $\xi (t)$ in the neighborhood of $t_0$. For Gaussian processes, this condition is also necessary. Some other problems connected with analytic processes are also investigated.