content_image/312679.jpg content_image/312676.jpg content_image/312680.jpg content_image/312674.jpg content_image/312678.jpg content_image/312677.jpg content_image/312675.jpg
Finally, combining (44), (45), and (46), we obtain for 

the following upper and lower bounds: 

<img src='content_image/312679.jpg'>

Let τ > 0 be an arbitrarily small number. Equations (37) and (41) imply that there exist ¯ M and ¯ M ′ such that, for any M > ¯ M and M ′ > ¯ M ′ , 

for all sufficiently large p. Let us choose M > ¯ M and M ′ > ¯ M ′ so that 

and 

<img src='content_image/312676.jpg'>

for all sufficiently large p, a.s.. Then, (48) implies that 

for all sufficiently large p , a.s.. Since τ can be chosen arbitrarily, we have, from (47) and (49), 

where o (1) → 0 as p → ∞ uniformly in { 2 θ$_{pj}$ ∈ Ω$_{εη}$ , j ≤ r } , a.s.. □ 

<img src='content_image/312680.jpg'>

<img src='content_image/312674.jpg'>

<img src='content_image/312678.jpg'>

<img src='content_image/312677.jpg'>

<img src='content_image/312675.jpg'>

