Show that where p () is defined in (5.4.2). To prove the results in (5.4.6a,b,c), it

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Show that 

et p* (t; r, q) = p* (t; rq,0),

where p(τ) is defined in (5.4.2). To prove the results in (5.4.6a,b,c), it suffices to consider the sign behavior of

where d dt p* (t; r, 0) = et f(t), f(t) = -rN(-d) + =n(-d), d = a, d=d +0 and  = 0Consider the following two cases (Dai, Kwok and Wu, 2004). 

(a) For r ≤ 0, show that

d -p* (t; r, 0) > 0. dt

(b) For r > 0, show that  

f'(t) = on(-d) 14+  2 [a (a + o) -  ]  T

hence deduce the results in (5.4.6b,c).

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