Nonlinear Transformations of Gaussian Processes

The article considers nonlinear transformations of Gaussian process $\xi(t)$ which have the form $\int_0^Tf(\xi(t))dt$ It is shown that for a certain class of Gaussian processes, $\xi(t)$ can specify the function $\mathbf I(x)=\int_0^T\delta(x+\xi(t))dt$, where $\delta(t)$ is the Dirac delta function. The properties of $\mathbf I(x)$ are studied.