An Equality in Stochastic Processes
UNIVERSITY OF CALIFORNIA, BERKELEY BERKELEY United States
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The equality presented in this paper is extremely simple, but has proven useful on a number of occasions in deriving certain transition probabilities where other approaches such as the Laplace transform or the generating function become untidy see, for example, 7. The equality is not completely unknown it has appeared, in a slightly different form, in a two dimensional process 2,p. 102 and it is obvious for the simple Poisson process. The purpose of this paper is to state it in a general form and to demonstrate its validity and usefulness with a number of examples.
- Statistics and Probability