First-order Asymptotics of the Mutant Sub-populations for an Infinite Mono-directional Grap

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First-order Asymptotics of the Mutant Sub-populations for an Infinite Mono-directional Grap
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In this paper, we aim to understand the evolution of the genetic composition of cancer cell populations.

This paper is available on arxiv under CC 4.0 license. Authors: Vianney Brouard, ENS de Lyon, UMPA, CNRS UMR 5669, 46 All´ee d’Italie, 69364 Lyon Cedex 07, France; E-mail: [email protected].

In particular it implies that Notice in particular that with such a construction it immediately follows the monotone coupling Denote by see Section 1.1, or Theorem 1. 3.1 The wild-type dynamics Using Ito’s formula and it follows Solving this equation we obtain for all t ≥ 0 Similarly we have Consequently combining , and gives that Finally we have which concludes the proof. Proof of Lemma 3.2.

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