A multiplicative stochastic measure diffusion process is the continuous analogue of an infinite particle branching diffusion process. In this paper the limiting behavior of the critical measure diffusion process is investigated. Conditions are found under which a non-trivial steady state random measure exists and in this case a spatial central limit theorem is established.

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Persistent URL dx.doi.org/10.1007/BF00532877
Journal Probability Theory and Related Fields
Citation
Dawson, D.A. (1977). The critical measure diffusion process. Probability Theory and Related Fields, 40(2), 125–145. doi:10.1007/BF00532877