DISCUSSION OF CONDITION (ii)

We return now to the condition of statistical independence of adjacent intervals. This implies that the joint probability f(vlt v2) = /(«1)/(«’2) where and »2 are values of the variable during two adjacent intervals and A2t, as illustrated in Fig. 2.14. We saw [following (2.6,30)] that statistical independence implies zero correlation. In the present context we may infer statistical independence from zero correlation. Thus we require that

= «Л = 0 (2.6,53)

the average being taken over the range 0 <t'< At. Now if we define a characteristic correlation time by

Fie. 2.14

as illustrated in Fig, 2.15, and require that At t*, then it is evident that condition (2.6,53) will be satisfied. Since the present results will normally be of interest only for large r and large tlt this condition can be met while still keeping n very large. I