Erratum to: Weak Convergence of a Mass-Structured Individual-Based Model

Erratum to: Appl Math Optim DOI 10.1007/s00245-014-9271-3

The author would like to correct the errors in the Original Publication.

• 1. Before the end of the Sect. 3.2 “Growth Flow”, the following text should be corrected:

  $$\begin{aligned} {\mathbb {M}}(\mathcal{X})=\cdots \end{aligned}$$

  should be replaced by

  $$\begin{aligned} \mathcal{M}(\mathcal{X})=\cdots \end{aligned}$$

• 2. The following text should be corrected of Proposition 4.6:

  • Last line of the Proposition 4.6:

    $$\begin{aligned} \ldots \,\,\,and\,\nu \in \mathcal{M}_F (\mathcal{X}). \end{aligned}$$

    should be replaced by

    $$\begin{aligned} \ldots \,\,\,and\,\nu \in \mathcal{M}(\mathcal{X}). \end{aligned}$$

  • Under Proposition 4.6 first line of proof:

    $$\begin{aligned} \ldots \,\,\,and\,\nu _0 =\nu \in \mathcal{M}_F (\mathcal{X}). \end{aligned}$$

    should be replaced by

    $$\begin{aligned} \ldots \,\,\,and\,\nu _0 =\nu \in \mathcal{M}(\mathcal{X}). \end{aligned}$$

  • Under Proposition 4.6 suppress the second line of proof:

    $$\begin{aligned} \hbox {First we suppose that } \nu \in \mathcal{M}(\mathcal{X}). \end{aligned}$$

  • Page 18, suppress the last paragraph of the proof.

• 3. Remark 5.6, third line from the bottom: something could be added after “$f\in C^1( \mathcal{X}).$” that is, replace:

and $f\in C^1( \mathcal{X}).$ Note that this generator has the same “substrat” part than that of the initial generator (12) which again justifies the Remark 5.1.

by

and $f\in C^1( \mathcal{X})$; $s\in {\mathbb {R}}_+$ and $\nu \in \mathcal{M}^n(\mathcal{X})=\{\frac{1}{n}\Sigma _{i=1}^N \delta _{x^i} ,;\,N\in {\mathbb {N}},\,x^i\,\in \,\,\,\mathcal{X}\}$. Note that this generator has the same “substrat” part than that of the initial generator (12) which again justifies the Remark 5.1.