Properties and applications of stochastic processes with stationarynth-order increments

Abstract

Many physical problems are described by stochastic processes with stationary increments. We present a general description of such processes. In particular we give an expression of a process in terms of its increments and we show that there are two classes of processes: diffusion and asymptotically stationary. Moreover, we show that thenth increments are given by a linear filtering of an arbitrary stationary process.