Corrigendum to “Large deviations for the Fleming-Viot process with neutral mutation and selection”

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 a The

Donald A. Dawsona; ∗ , Shui Fengb 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 ÿnitely additive, nonnegative, mass one measures on E. Every element  in X has the following unique decomposition:  = ac + s + p ; where p is a pure ÿnite additive measure, ac and s are both countably additive with ac 0 ; s ⊥0 . A nonnegative ÿnite additive measure is called pure ÿnite 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   ÂH (0 |ac ) if  0 ;  6∈ M1 (E); I () = ÂH (0 |) if  0 ;  ∈ M1 (E);  ∞ else: Theorems 2:5 and 3:4 should be modiÿed accordingly. All calculations about the inÿnite dimensional LDP hold true for probability-valued paths. We thank W. Stannat for pointing out the deÿciency.

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PII of the original article: S0304-4149(98)00035-0 Corresponding author. E-mail address: don@ÿelds.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