Uniform convergence of proliferating particles to the FKPP equation

Flandoli, Franco; Leimbach, Matti; Olivera, Christian

doi:10.48550/arxiv.1604.03055

Cited by 1 publication

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“…The first one is that branching occurs also along the vessels; there is now a spatial density rate and it is less easy to relate this variable density rate with a constant upper bound of Yule type. This is made even more difficult by the presence of the factor |v| in the branching rates, a factor that is a priori unbounded (see (15), and ( 16)). We thus have to work much more than in the classical case.…”

Section: Upper Bound On the Number Of Particlesmentioning

confidence: 99%

On the mean field approximation of a stochastic model of tumor-induced angiogenesis

Capasso,

Flandoli

2017

Preprint

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In the field of Life Sciences it it very common to deal with extremely complex systems, from both analytical and computational points of view, due to the unavoidable coupling of different interacting structures. As an example, angiogenesis has revealed to be an highly complex, and extremely interesting biomedical problem, due to the strong coupling between the kinetic parameters of the relevant branching -growth -anastomosis stochastic processes of the capillary network, at the microscale, and the family of interacting underlying biochemical fields, at the macroscale. In this paper an original revisited conceptual stochastic model of tumor driven angiogenesis has been proposed, for which it has been shown that it is possible to reduce complexity by taking advantage of the intrinsic multiscale structure of the system; one may keep the stochasticity of the dynamics of the vessel tips at their natural microscale, whereas the dynamics of the underlying fields is given by a deterministic mean field approximation obtained by an averaging at a suitable mesoscale. While in previous papers only an heuristic justification of this approach had been offered, in this paper a rigorous proof is given of the so called "propagation of chaos", which leads to a mean field approximation of the stochastic relevant measures associated with the vessel dynamics, and consequently of the underlying TAF field. As a side though

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Section: Upper Bound On the Number Of Particlesmentioning

confidence: 99%