Stochastic p.d.e.’s arising from the long range contact and long range voter processes. (English) Zbl 0827.60050
Summary: A long range contact process and a long range voter process are scaled so that the distance between sites decreases and the number of neighbors of each site increases. The approximate densities of occupied sites, under suitable time scaling, converge to continuous space time densities which solve stochastic p.d.e.’s. For the contact process the limiting equation is the Kolmogorov-Petrovskij-Piskunov equation driven by branching white noise. For the voter process the limiting equation is the heat equation driven by Fisher-Wright white noise.
MSC:
| 60H25 | Random operators and equations (aspects of stochastic analysis) |
| 35R60 | PDEs with randomness, stochastic partial differential equations |
Keywords:
long range contact process; long range voter process; Kolmogorov- Petrovskij-Piskunov equation; branching white noiseReferences:
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