Directory UMM :Data Elmu:jurnal:S:Stochastic Processes And Their Applications:Vol88.Issue1.2000:
Stochastic Processes and their Applications 88 (2000) 175
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Corrigendum
Corrigendum to “Large deviations for the Fleming-Viot
process with neutral mutation and selection”
[Stochastic Proc. Appl. 77 (1998) 207–232]1
Donald A. Dawsona; ∗ , Shui Fengb
a The
Fields Institute, 222 College Street, Toronto, Ont., Canada M5T 3J1
b McMaster University, Hamilton, Ont., Canada L8S 4K1
The space X in Section 2 is the space of all nitely additive, nonnegative, mass one
measures on E. Every element in X has the following unique decomposition:
= ac + s + p ;
where p is a pure nite additive measure, ac and s are both countably additive with
ac .0 ; s ⊥0 . A nonnegative nite additive measure is called pure nite additive if
there is no nonzero, nonnegative, countably additive measure that is less than it. An
element in X is a probability measure if and only if p (E) = 0. Thus X is strictly
bigger than M1 (E) (even though every element of X can be associated to a continuous
linear functional on C([0; 1])). Thus, we need to change the space M1 (E) in Theorem
2:4 to X, and the rate function is given by
H (0 |ac ) if .0 ; 6∈ M1 (E);
I () = H (0 |)
if .0 ; ∈ M1 (E);
∞
else:
Theorems 2:5 and 3:4 should be modi ed accordingly. All calculations about the in nite
dimensional LDP hold true for probability-valued paths.
We thank W. Stannat for pointing out the de ciency.
1
PII of the original article: S0304-4149(98)00035-0
Corresponding author.
E-mail address: don@ elds.utoronto.ca (D.A. Dawson)
∗
c 2000 Published by Elsevier Science B.V. All rights reserved.
0304-4149/00/$ - see front matter
PII: S 0 3 0 4 - 4 1 4 9 ( 9 9 ) 0 0 1 2 3 - 4
www.elsevier.com/locate/spa
Corrigendum
Corrigendum to “Large deviations for the Fleming-Viot
process with neutral mutation and selection”
[Stochastic Proc. Appl. 77 (1998) 207–232]1
Donald A. Dawsona; ∗ , Shui Fengb
a The
Fields Institute, 222 College Street, Toronto, Ont., Canada M5T 3J1
b McMaster University, Hamilton, Ont., Canada L8S 4K1
The space X in Section 2 is the space of all nitely additive, nonnegative, mass one
measures on E. Every element in X has the following unique decomposition:
= ac + s + p ;
where p is a pure nite additive measure, ac and s are both countably additive with
ac .0 ; s ⊥0 . A nonnegative nite additive measure is called pure nite additive if
there is no nonzero, nonnegative, countably additive measure that is less than it. An
element in X is a probability measure if and only if p (E) = 0. Thus X is strictly
bigger than M1 (E) (even though every element of X can be associated to a continuous
linear functional on C([0; 1])). Thus, we need to change the space M1 (E) in Theorem
2:4 to X, and the rate function is given by
H (0 |ac ) if .0 ; 6∈ M1 (E);
I () = H (0 |)
if .0 ; ∈ M1 (E);
∞
else:
Theorems 2:5 and 3:4 should be modi ed accordingly. All calculations about the in nite
dimensional LDP hold true for probability-valued paths.
We thank W. Stannat for pointing out the de ciency.
1
PII of the original article: S0304-4149(98)00035-0
Corresponding author.
E-mail address: don@ elds.utoronto.ca (D.A. Dawson)
∗
c 2000 Published by Elsevier Science B.V. All rights reserved.
0304-4149/00/$ - see front matter
PII: S 0 3 0 4 - 4 1 4 9 ( 9 9 ) 0 0 1 2 3 - 4