Limit theorems for the number of crossings of a fixed plane by certain sequences of generalized diffusion processes (Q1905099)

The article is concerned with a weak convergence of generalized diffusion processes to limit ones. The approach is based on using the number of crossings of a fixed plane by a discrete approximation of a process, i.e., by the sequence \(x(0), x(n^{-1}), x(2n^{-1}), \dots,\) where \(n\) is a positive integer. The most part of the article is devoted to the case of \(R^d\)-valued processes \((d > 1)\). Some results for the case \(d = 1\) have been stated as well. It has been established that the relation between the rate of weak convergence to the limit process and the rate of decreasing to zero of the process discretization step substantially affects the limit distribution.