Behavior of limiting diffusions for density-dependent branching processes
C Wofsy - Biological Growth and Spread: Mathematical Theories …, 1980 - Springer
C Wofsy
Biological Growth and Spread: Mathematical Theories and Applications …, 1980•SpringerA sequence of density-dependent analogues of continuous time branching processes is
shown to converge weakly to a diffusion. The diffusion has infinitesimal mean displacement
(drift) λxα (x) and infinitesimal variance 2λxβ, where λ and β are positive constants and α is a
bounded, continuous, real-valued function on [0,∞). Boundary behavior of the diffusion is
studied, in the case where α (x) is negative for large enough x values. This corresponds to a
“controlled” population in which growth is retarded when the population is too large.
shown to converge weakly to a diffusion. The diffusion has infinitesimal mean displacement
(drift) λxα (x) and infinitesimal variance 2λxβ, where λ and β are positive constants and α is a
bounded, continuous, real-valued function on [0,∞). Boundary behavior of the diffusion is
studied, in the case where α (x) is negative for large enough x values. This corresponds to a
“controlled” population in which growth is retarded when the population is too large.
Abstract
A sequence of density-dependent analogues of continuous time branching processes is shown to converge weakly to a diffusion. The diffusion has infinitesimal mean displacement (drift) λxα(x) and infinitesimal variance 2λxβ, where λ and β are positive constants and α is a bounded, continuous, real-valued function on [0,∞). Boundary behavior of the diffusion is studied, in the case where α(x) is negative for large enough x values. This corresponds to a “controlled” population in which growth is retarded when the population is too large.
Springer
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