Pukhov, G. E.; Vojtenkov, I. N. Differential transformations of random functions. (English. Russian original) Zbl 0708.60063 Sov. Phys., Dokl. 35, No. 2, 111-112 (1990); translation from Dokl. Akad. Nauk SSSR 310, No. 4, 810-813 (1990). Let X(\(\omega\),t) be a stochastic process. A direct stochastic differential transformation is introduced by \[ X(\omega,K)=\Phi (K)[\partial^ KX(\omega,t)/\partial t^ K]_{t=t_ j},\quad K=0,1,2,..., \] where \(\Phi\) (K) is a weight function. The inverse stochastic differential transformation is given in series form: \[ X(t)=[(1/K!)\sum^{\infty}_{K=0}(t-t_ j)^ K X(K)]/q(t), \] where q(t) is a kernel of the transformations. The author computes the moment functions of stochastic processes on the basis of stochastic differential transformations. Further a representation of random states is given by means of the discrete entity. Reviewer: W.Grecksch MSC: 60H99 Stochastic analysis 93E03 Stochastic systems in control theory (general) Keywords:state representation; stochastic differential transformations PDFBibTeX XMLCite \textit{G. E. Pukhov} and \textit{I. N. Vojtenkov}, Sov. Phys., Dokl. 35, No. 2, 111--112 (1990; Zbl 0708.60063); translation from Dokl. Akad. Nauk SSSR 310, No. 4, 810--813 (1990)