Abstract P-625

MATH 625 Homework VI

1. Proof. (a) It is known that all finite dimensional distributions of X(t) are multivariate normal with E(X(s)) = 0 and E(X(s)X(t)) = min{s, t}. It is easy to see that B(t) ∼ N(0, t), B(t′)−B(t) = X(s+ t′)−X(s+ t) ∼ N(0, t′− t) (t′ > t) and B(t0), B(t1) − B(t0), ..., B(tn) − B(tn−1) are independent. Hence all finite dimensional distributions of B(t) are multivariate normal with E(B(t)) = 0. Su...

MATH 625 Homework V

MATH 625 Assignment 2

625-628 Conflict

625 IRAQ, Afghanistan, Kosovo, Bosnia, Somalia, Mozambique, Indonesia – all countries that have suffered or are currently suffering from the effects of conflict or natural disaster, and all countries where veterinary expertise has been required. While media images from such areas primarily focus on the human cost, livestock and draught animals are often an essential part of the lives of the peo...

MATH 625 Homework IV

1. Proof. (a) Let x ∈ [0, 1] and δ > 0, we want to show that there exist n such that nλ mod 1 ∈ (x−δ, x+δ), for which it suffices to show that there exists n0 and y ∈ (−δ, δ) such that n0λ ≡ y (mod 1). Then take n to be an appropriate multiple of n0. To prove the reduced proposition, choose m such that 10−m < δ. Note that there exist n1 < n2 such that (n1λ mod 1) and (n2λ mod 1) have the same f...