ABSTRACT

Recall that (Ω,F , P ) is a complete probability space. The elements of Euclidean space Rk will be viewed as column vectors and we denote the dot product on Rk by (t, x) or t · x, that is,

(t, x) = t · x = ∑kj=1 tjxj , for all vectors t = (t1, t2, . . . , tk)′, x = (x1, x2, . . . , xk)′ ∈ Rk. Here the prime denotes transposition as usual. Let { e1, e2, . . . , ek } denote the standard basis of Rk.