Directory UMM :Data Elmu:jurnal:S:Stochastic Processes And Their Applications:Vol88.Issue1.2000:

Stochastic Processes and their Applications 88 (2000) 175

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. Dawson

a;∗

_{, Shui Feng}

b

a_{The Fields Institute, 222 College Street, Toronto, Ont., Canada M5T 3J1}

b_{McMaster University, Hamilton, Ont., Canada L8S 4K1}

The spaceX _{in Section 2 is the space of all nitely additive, nonnegative, mass one}

measures onE. Every element in X _{has the following unique decomposition:}

=ac+s+p;

wherep is a pure nite additive measure, ac ands 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 thanM1(E) (even though every element ofX 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}

I() =  



H(0|ac) if .0; 6∈M1(E);

H(0|) if .0; ∈M1(E);

∞ else:

Theorems 2:5 and 3:4 should be modied accordingly. All calculations about the innite dimensional LDP hold true for probability-valued paths.

We thank W. Stannat for pointing out the deciency.

1_{PII of the original article: S0304-4149(98)00035-0} ∗_{Corresponding author.}

E-mail address:don@elds.utoronto.ca (D.A. Dawson)