ABSTRACT
The general theory of stochastic processes had its origin in the fundamental papers of the Russian mathematicians A. N. Kolmogorov and A. YA. Khinchine. Demands of physical statistics and a number of engineering fields have posed a great number of new problems for probability theory outside of the framework of the classical theory. The physicists and engineers were interested in studying processes, that is, phenomena that changed with time. The stochastic process is called the Birth and Death Processes. The distribution function of any homogeneous stochastic process with independent increments is infinitely divisible. Khinchine has separated an important class of stochastic processes with aftereffect, the so-called stationary processes, which behave homogeneously with time. The normal stochastic process thus defined is stationary both in the wide and in the strict senses. The possibility of decomposing an arbitrary stochastic process which is stationary in the wide sense into the form was indicated by Kolmogorov in 1940.
