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

DOI10.1017/S0956792518000347zbMath1429.92040arXiv1708.03830OpenAlexW2963236466WikidataQ129686689 ScholiaQ129686689MaRDI QIDQ5205839

Franco Flandoli, Vincenzo Capasso

Publication date: 16 December 2019

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.03830

zbMATH Keywords

convergence of probability measuresinteracting particle systemsstochastic analysiscell movementPDEs in connection with biology and other natural sciences

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Martingales with continuous parameter (60G44) Developmental biology, pattern formation (92C15) Cell movement (chemotaxis, etc.) (92C17)

Related Items

A coupled stochastic differential reaction-diffusion system for angiogenesis, Hydrodynamic limit of a stochastic model of proliferating cells with chemotaxis, Ergodic Behaviour of a Multi-Type Growth-Fragmentation Process Modelling the Mycelial Network of a Filamentous Fungus, The mathematical modeling of cancer growth and angiogenesis by an individual based interacting system, A convergent numerical scheme for integrodifferential kinetic models of angiogenesis, Two dimensional soliton in tumor induced angiogenesis, A mean-field approach to self-interacting networks, convergence and regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies
• Lattice and non-lattice models of tumour angiogenesis
• On the mathematical modelling of tumor-induced angiogenesis
• Stochastic modelling of tumour-induced angiogenesis
• Semigroups of linear operators and applications to partial differential equations
• On the derivation of reaction-diffusion equations as limit dynamics of systems of moderately interacting stochastic processes
• Point processes and queues. Martingale dynamics
• Continuous and discrete mathematical models of tumor-induced angiogenesis
• Infinite-dimensional dynamical systems in mechanics and physics.
• Mathematical modeling of tumor-induced angiogenesis
• A hybrid discrete-continuum mathematical model of pattern prediction in the developing retinal vasculature
• On stochastic distributions and currents
• Methods of small parameter in mathematical biology
• Invasion and adaptive evolution for individual-based spatially structured populations
• Regularity of stochastic kinetic equations
• On the Geometric Densities of Random Closed Sets