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Microscopic and Mezoscopic Models for Mass Distributions

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Stochastic Dynamics

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Abstract

In this paper we extend the derivation of mezoscopic partial differential equations (or stochastic partial differential equations (SPDE’s)) from particle systems with finite conserved mass to infinite conserved mass. We also sketch the history of stochastic and deterministic (i.e., mezoscopic and macroscopic) reaction-diffusion models initiated by Arnold’s work as well as some results of Dawson’s measure processes approach to SPDE’s. At the end of the paper we show how to include creation and annihilation through a fractional step method into the mezoscopic PDE’s.

This contribution is dedicated to Professor Ludwig Arnold on the occasion of his 60th birthday. It was supported by NSF grants DMS-9703648 and DMS-9414153.

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Kotelenez, P. (1999). Microscopic and Mezoscopic Models for Mass Distributions. In: Stochastic Dynamics. Springer, New York, NY. https://doi.org/10.1007/0-387-22655-9_17

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  • DOI: https://doi.org/10.1007/0-387-22655-9_17

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-98512-1

  • Online ISBN: 978-0-387-22655-2

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