Then, (42) and (93) yield f T α 1 / t ( x ) = t sin ( π α ) π α x t − 1 E [ e − x X c , t ] = t sin ( π α ) π α x t − 1 E [ ( X c , t ) t ( X c , t ) − t e − x X c , t ] = t sin ( π α ) π α E...
Proof. Lemmas 6 and 8 yield the lemma immediately. □ Regarding Lemma 12, the following theorem can be proved: Theorem 3. (19) and (20) in Lemma 12 holds true for 1 ≦ n ≦ 4 . Proof. We prove that (19) and (20) in Lemma 12 hold for 1 ≦ n ≦ 4 in a straightforward ...
some estimates on the value function yield that −𝑉(𝑥,𝑖)=inf𝐽(𝑝1,…,𝑝𝑁),−V(x,i)=infJp1,…,pN, (9) where 𝑥=(𝑥1,…,𝑥𝑁)∈ℝ𝑁x=x1,…,xN∈RN assumes values (𝑦1(0),…,𝑦𝑁(0)).(y10,…,yN0). Once such a function is found,...