Abstract
In its present shape the limit theory for critical, irreducible Markov branching processes with arbitrary set of types and finite second moments [1],[2] does not apply to branching diffusion processes with absorbing barriers. The occurrence of absorbing barriers is incompatible with the condition of uniform positivity imposed on one of the eigenfunctions associated with the moment semigroup. Taking into account certain asymptotic spectral properties of the differential operator generating the moment semigroup of a branching diffusion process, the deficiency can be overcome—at least to some extent—by a modification of the treatment given in [2]. We demonstrate this for a branching process of Brownian particles restricted to a one-dimensional finite interval with totally absorbing barriers at the endpoints.
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