Directory UMM :Data Elmu:jurnal:S:Stochastic Processes And Their Applications:Vol92.Issue2.2001:
Stochastic Processes and their Applications 92 (2001) 355
www.elsevier.com/locate/spa
Erratum
Erratum to “Pairs of renewal processes whose superposition
is a renewal process”
[Stochastic Process. Appl. 86 (2000) 217–230]
J.A. Ferreira
Mitthogskolan, Institutionen for fysik och matematik, 851 70 Sundsvall, Sweden
Received 9 May 2000; accepted 28 September 2000
The proof of (d) in Section 3 makes no sense. The following proof should replace
the whole sentence ‘Second, replacing ...’.
Using the continuity of F and G in (0; ), we can prove that F and G are continuous on (0; 2) by showing that they are continuous at each u + v with u; v ∈ (0; ).
Subtracting from both sides of (22) the corresponding expressions with u + v− and v−
in place of u + v and v, and using F(v−)
= F(v),
G(v−)
= G(v),
we nd
+ v−) − G(u
+ v)]F(v);
+ v) − F(u
+ v−)] = (u)[G(u
G(v)[
F(u
+ v−) =
+ v) = F(u
+ v−) and G(u
hence (one side being 6 0 and the other ¿ 0) F(u
+ v) for u; v ∈ (0; ). This argument extends to u; v ∈ (0; n) ∩ (0; x+ ), n ∈ N, and
G(u
hence to (0; x+ ).
Two smaller mistakes: In the proof of (a), Section 2, ‘m1 (t) + m2 (t) = m(t)’ should
be replaced by ‘m1 (t) + m2 (t) = m1 (t)’; in the last paragraph of Section 3, ‘in the
is a pleonasm because the set is open.
interior of (0; x+ ) − D’
PII of the original article: S0304-4149(99)00095-2.
E-mail address: [email protected] (J.A. Ferreira).
c 2001 Elsevier Science B.V. All rights reserved.
0304-4149/01/$ - see front matter
PII: S 0 3 0 4 - 4 1 4 9 ( 0 0 ) 0 0 0 7 6 - 4
www.elsevier.com/locate/spa
Erratum
Erratum to “Pairs of renewal processes whose superposition
is a renewal process”
[Stochastic Process. Appl. 86 (2000) 217–230]
J.A. Ferreira
Mitthogskolan, Institutionen for fysik och matematik, 851 70 Sundsvall, Sweden
Received 9 May 2000; accepted 28 September 2000
The proof of (d) in Section 3 makes no sense. The following proof should replace
the whole sentence ‘Second, replacing ...’.
Using the continuity of F and G in (0; ), we can prove that F and G are continuous on (0; 2) by showing that they are continuous at each u + v with u; v ∈ (0; ).
Subtracting from both sides of (22) the corresponding expressions with u + v− and v−
in place of u + v and v, and using F(v−)
= F(v),
G(v−)
= G(v),
we nd
+ v−) − G(u
+ v)]F(v);
+ v) − F(u
+ v−)] = (u)[G(u
G(v)[
F(u
+ v−) =
+ v) = F(u
+ v−) and G(u
hence (one side being 6 0 and the other ¿ 0) F(u
+ v) for u; v ∈ (0; ). This argument extends to u; v ∈ (0; n) ∩ (0; x+ ), n ∈ N, and
G(u
hence to (0; x+ ).
Two smaller mistakes: In the proof of (a), Section 2, ‘m1 (t) + m2 (t) = m(t)’ should
be replaced by ‘m1 (t) + m2 (t) = m1 (t)’; in the last paragraph of Section 3, ‘in the
is a pleonasm because the set is open.
interior of (0; x+ ) − D’
PII of the original article: S0304-4149(99)00095-2.
E-mail address: [email protected] (J.A. Ferreira).
c 2001 Elsevier Science B.V. All rights reserved.
0304-4149/01/$ - see front matter
PII: S 0 3 0 4 - 4 1 4 9 ( 0 0 ) 0 0 0 7 6 - 4