On the extrapolation of entire functions observed in a Gaussian white noise (Q2722151)

The problem of extrapolation of entire analytic functions from ``noised'' observations is considered. Namely, the observed random process \(X_{\varepsilon}(t)\) is described by the equation \(dX_{\varepsilon}(t)=f(t) dt+\varepsilon dw(t),\) where \(f(z)\) is an entire function, \(w(t)\) is a Wiener process, \(a\leq t\leq b.\) The problem is to renew the values \(f(z)\) of the function \(f\) at the point \(z\) of the complex plane from observations of \(X_{\varepsilon}(t).\) A solution to the problem of extrapolation of analytic functions from a certain class in the case of observations with a white noise of not high intensity is presented.