By Ishiguro M., Sakamoto Y.

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I'--".. 1. M"'. r / Analytic and Empirical Evidences of Isoperimetric Processes 23 We define the au hypothesis or model of stock prices by stating that V is an arnstein- Uhlenbec~ process. Actually under the au it will often only be used that V is stationary, ergodic, and Gaussian. The Brownian motion model of stock prices implies the au in equilibrium. The converse is true if p = corr[V(n), V(n + 1)] and only then. d. g. [24]). To examine the au it could be natural to delete a few terms in the very beginning of the series but we will not do that here.

L. Jennergren and P. Toft-Nielsen, An in1Jelfigation oJ random wlllJ:. tock market, Nation~konomisk Tidsskrift 115 (1977), 254-269. A. S. , Journal of the American Statistical Association 70 (1975),690-697. A. 8 (1967). O. Praetz, The di6tribution of 6hare price changes, Journal of Business 45 (1972), 49-55. A. Samuelson, Mathematics of speculative price, SIAM Rev XX (1973), 1-42. [20] D. Slepian, The one-6ided barrier problem for Gauuian noise, The Bell System Technical Journal 41 (1962), 463-501.

2. {Vt E T, n {X(s), s E B(t, e) £>0 n S} i: 0} = 1.