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Extra info for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono

Example text

8), the proof is complete. Put fs,x := log 1 + (t − s)−1 log 1 + |x|−1 1{x=0} 1{s 0 and q > 0. 14) where := 1 + q. 15) Proof. 16) where in the last step we have used the classical Markov inequality. 17) . 18) (q) (recall that t isfixed). 19) (q). 19) instead of c. 16), the proof is complete. 4. Fix X0 = μ ∈ Mf \{0}. Let d = 1. Let ε > 0 and γ ∈ 0, (1+ β )−1 .

Using the assumption t − s ≥ 2−2n nρ , we arrive at the inequality 2+ξ Δ Ln− [rδ(s,y) ] ≤ C 2−η¯ c n 1+β +2q+ ρ2 (η¯ c −2) . ξ )/(1+β )) From this we see that if we choose ρ ≥ 2(2q+(2+ , then the jumps of Ln− are 2−η¯ c bounded by C 2−η¯ c n , and hence Un1 does not occur. 2) from Appendix A, one can easily derive (qt−s (c2−n−2 , 0))− ≤ C2−n (t − s)−1 . Then for y ∈ −(t − s)1/2 logξ (t − s)−1 , c 2−n−3 and t − s ≤ 2−2n n−ρ we have the inequality 1 Δ Ln− [rδ(s,y) ] ≤ C2−n (t − s)−1 (|y|(t − s)) 1+β ( fs,y ) 3 ≤ C2−n (t − s) 2(1+β ) −1 2+ξ +2q (t − s)−1 2+ξ +2q (t − s)−1 log 1+β = C2−n (t − s)(η¯ c −1)/2 log 1+β 2+ξ −ρ (η¯ c −1)/2+ 1+ +2q β ≤ C2−η¯ c n n Choosing ρ ≥ 2(ξ +2+2q(1+β )) (1+β )(η¯ c −1) , .

25) Regularity and irregularity of superprocesses with (1 + β )-stable branching mechanism 31 Furthermore, if |y| ≥ 2 and (t − s) ≤ c−2 , then pt−s c (t − s)1/2 − y ≤ pt−s (1) = (t − s)−1/2 p1 (t − s)−1/2 = (2π )−1/2 (t − s)−1/2 e−1/2(t−s) . This implies that R\B2 (0) dy pt−s c (t − s)1/2 − y Xs (y) ≤ (2π )−1/2 (t − s)−1/2 e−1/2(t−s) Xs (R) ≤ Cc−2 Xs (R). 25), we obtain | y−c (t−s)1/2 |> 2c (t−s)1/2 dy pt−s c (t − s)1/2 − y Xs (y) ≤ Cc−2 WB3 (0) + sup Xs (R) . 0

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A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono by Yasui Y.


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