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If a variable assumes the discrete values xj (j = 1, 2, 3, …) with specified probabilities f(xj), where 
f(xj) it is said to be a discrete 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 a discrete random process.
A class of discrete random processes of particular interest to the pure mathematician and to the mathematical statistician has been called stochastically definite by Kolmogoroff (1931). Such a random process is distinguished by the fact that the probability that the random variable concerned assumes a given value n at time t depends only on the value m assumed by the variable at time s (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 value n at time t in the form Pmn (s, t).
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- Copyright © Institute of Actuaries Students' Society 1949
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Being the substance of a contribution to the University of Toronto's mathematical colloquium held on 12 October 1948.
References
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