ON THE CONSTRUCTION AND SUPPORT PROPERTIES OF MEASURE-VALUED DIFFUSIONS ON D⊆Rd WITH SPATIALLY DEPENDENT BRANCHING1

نویسنده

  • Ross G. Pinsky
چکیده

L = 1 2∇ · a∇ + b · ∇ on D ⊆ R and whose spatially dependent branching term is of the form β x z − α x z2, x∈D where β satisfies a very general condition and α > 0. In the case that α and β are bounded from above, we show that the measurevalued process can also be obtained as a limit of approximating branching particle systems. We give criteria for extinction/survival, recurrence/transience of the support, compactness of the support, compactness of the range, and local extinction for the measure-valued diffusion. We also present a number of examples which reveal that the behavior of the measure-valued diffusion may be dramatically different from that of the approximating particle systems.

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تاریخ انتشار 2001