Random creation and dispersion of mass

Aubrey Wulfsohn

Journal of Multivariate Analysis, 1986, vol. 18, issue 2, 274-286

Abstract: Consider evolution of density of a mass or a population, geographically situated in a compact region of space, assuming random creation-annihilation and migration, or dispersion of mass, so the evolution is a random measure. When the creation-annihilation and dispersion are diffusions the situation is described formally by a stochastic partial differential equation; ignoring dispersion make approximations to the initial density by atomic measures and if the corresponding discrete random measures converge "in law" to a unique random measure call it a solution. To account for dispersion Trotter's product formula is applied to semiflows corresponding to dispersion and creation-annihilation. Existence of solutions has been a conjecture for several years despite a claim in ([2], J. Multivariate Anal. 5, 1-52). We show that solutions exist and that non-deterministic solutions are "smeared" continuous-state branching diffusions.

Keywords: Measure-valued; process; stochastic; differential; equation; transition; probability; vague; topology; narrow; topology; branching; Markov; process; immigration; nonlinear; semiflow; on; Banach; space; Trotter's; product; formula; infinitely; decomposable; continuous-state; branching; test; function (search for similar items in EconPapers)
Date: 1986
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