Martin Friesen

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Articles: 2

Evolution of states and mesoscopic scaling for two-component birth-and-death dynamics in continuum

Martin Friesen, Oleksandr Kutoviy

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 4, 346-374

Two coupled spatial birth-and-death Markov evolutions on $\mathbb{R}^d$ are obtained as unique weak solutions to the associated Fokker-Planck equations. Such solutions are constructed by its associated sequence of correlation functions satisfying the so-called Ruelle-bound. Using the general scheme of Vlasov scaling we are able to derive a system of non-linear, non-local mesoscopic equations describing the effective density of the particle system. The results are applied to several models of ecology and biology.

Non-autonomous interacting particle systems in continuum

Martin Friesen

↓ Abstract   |   Article (.pdf)

Methods Funct. Anal. Topology 22 (2016), no. 3, 220-244

A conservative Feller evolution on continuous bounded functions is constructed from a weakly continuous, time-inhomogeneous transition function describing a pure jump process on a locally compact Polish space. The transition function is assumed to satisfy a Foster-Lyapunov type condition. The results are applied to interacting particle systems in continuum, in particular to general birth-and-death processes (including jumps). Particular examples such as the BDLP and Dieckmann-Law model are considered in the end.

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