Discrete random Processes
If a variable assumes the discrete valuesxj(j= 1, 2, 3, …) with specified probabilitiesf(xj), wheref(xj) it is said to be adiscrete random variable. If a discrete random variable is also a function of a continuous (non-random) variable, for convenience usually assumed to be ‘time’, it is called adiscrete random process.A class of discrete random processes of particular interest to the pure mathematician and to the mathematical statistician has been calledstochastically definiteby Kolmogoroff (1931). Such a random process is distinguished by the fact that the probability that the random variable concerned assumes a given valuenat timetdepends only on the valuemassumed by the variable at times(s < t) and not on the values assumed at any intermediate or earlier points of time. This circumstance is allowed for by writing the probability of the valuenat timetin the form Pmn(s, t).