Anatolii Vladimirovich Skorokhod (On His 70th Birthday)

Ukrainian Mathematical Journal -     

A. V. Skorokhod's investigations in the area of limit theorems for random processes and the theory of stochastic differential equations

A survey of basic works of A. V. Skorokhod in the following fields of probability theory is presented: limit theorems for random processes, stochastic differential equations, theory of Markov processes.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 9, pp. 1157–1170, September, 1990.     

On Renewal Equations Appearing in Some Problems in the Theory of Generalized Diffusion Processes

We construct a Wiener process on a plane with semipermeable membrane located on a fixed circle and acting in the normal direction. The construction method takes into account the symmetry properties of both the circle and the Wiener process. For this reason, the method is reduced to the perturbation of a Bessel process by a drift coefficient that has the type of a δ-function concentrated at a point. This leads to a pair of renewal equations, using which we determine the transition probability of the radial part of the required process. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1302–1312, September, 2005.