The volume Stochastic Processes by K. Itรถ was published as No. 16 of Lecture Notes Series from Mathematics Institute, Aarhus University in August, 1969, based on Lectures given at that Institute during the academie year 1968ยญ 1969. The volume was as thick as 3.5 cm., mimeographed from typewritten manuscript and has been out of print for many years. Since its appearance, it has served, for those abIe to obtain one of the relatively few copies available, as a highly readable introduetion to basic parts of the theories of additive processes (processes with independent increments) and of Markov processes. It contains, in particular, a clear and detailed exposition of the Lรฉvy-It รถ decomposition of additive processes. Encouraged by Professor It รณ we have edited the volume in the present book form, amending the text in a number of places and attaching many footnotes. We have also prepared an index. Chapter 0 is for preliminaries. Here centralized sums of independent ranยญ dom variables are treated using the dispersion as a main tooI. Lรฉvy's form of characteristic functions of infinitely divisible distributions and basic properยญ ties of martingales are given. Chapter 1 is analysis of additive processes. A fundamental structure theยญ orem describes the decomposition of sample functions of additive processes, known today as the Lรฉvy-Itรณ decomposition. This is thoroughly treated, asยญ suming no continuity property in time, in a form close to the original 1942 paper of Itรณ, which gave rigorous expression to Lรฉvy's intuitive understanding of path behavior
