Omarov, S. O. On interpolation of a random process with the use of the values and the derivatives of the process at the interpolation nodes. (English. Russian original) Zbl 0628.60049 Theory Probab. Math. Stat. 32, 103-107 (1986); translation from Teor. Veroyatn. Mat. Stat. 32, 94-99 (1985). The Kotel’nikov-Shannon interpolation formula shows that a stationary random process with bounded spectrum can be recovered without error from observations on a certain infinite sequence of interpolation nodes. In this paper the Kotel’nikov-Shannon formula is generated to the case when observations of the process and its derivatives are taken on periodically repeating groups of nodes. It is proved that the interpolation formula converges with probability 1. Reviewer: M.Mirzahmedov Cited in 1 Document MSC: 60G10 Stationary stochastic processes 65D05 Numerical interpolation Keywords:stationary random process with bounded spectrum; interpolation; Kotel’nikov-Shannon formula; periodically repeating groups of nodes PDFBibTeX XMLCite \textit{S. O. Omarov}, Theory Probab. Math. Stat. 32, 103--107 (1986; Zbl 0628.60049); translation from Teor. Veroyatn. Mat. Stat. 32, 94--99 (1985)