Law of large numbers for super-Brownian motions with a single point source

Robert Grummt and Martin Kolb

Stochastic Processes and their Applications, 2013, vol. 123, issue 4, 1183-1212

Abstract: We investigate the super-Brownian motion with a single point source in dimensions 2 and 3 as constructed by Fleischmann and Mueller in 2004. Using analytic facts we derive the long time behavior of the mean in dimensions 2 and 3 thereby complementing previous work of Fleischmann, Mueller and Vogt. Using spectral theory and martingale arguments we prove a version of the strong law of large numbers for the two dimensional superprocess with a single point source and finite variance.

Keywords: Super-Brownian motion with singular mass creation; Strong law of large numbers; Expected mass; Schrödinger equation with point interaction (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:4:p:1183-1212

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DOI: 10.1016/j.spa.2012.12.002

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