Jean Casey Hypnosis and Meditation

Appendix 7B Proof of Eqs 764 and 765

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Here we prove, for a Gaussian stochastic processes z(t) and a general function of time x(t) the results (7.64) and (7.65). Our starting point is (cf. Eq. (7.63))

e'T,jxjzA = jT.jX (zj >-(1/2)EjEkxj (Szi Szk )xk (7.119)

where the sums are over the n random variables. Noting that this relationship holds for any set of constants {xj}, we redefine these constants by setting

and take the limit Atj ^ 0 and n in the interval to < t1 < t2 < ••• < tn. Then n \