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In section 3 we will give another application of the q-Taylor series in the field of the so–called integer-valued entire functions and give a first answer on a question asked by
On the other hand, Feller’s branching diffusion is a special case of the general continuous state branching processes (CSBP’s) initially studied by Jiˇrina [19], Lamperti [22, 23],
Keywords: Duality, graphical representation, Feller’s branching diffusion, branching-coalescing particle process, resampling-selection model, stochastic population
Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and
The proof of this lemma would follow by the same arguments as the proof of Lemma 3.1 of [5], applying the criterion for absolute continuity of the supremum of a Gaussian
(2) Branching Mechanism Reconstruction: By reconstruction of the branching mech- anism, the variable coefficient σ ( x ) of the branching generator is transformed as a
On the particle level we may take the view of having a trivial spatial motion (particles are fixed inbetween the discrete branching points) and non-local branching, whereas
Furthermore, the criterion applies to two important classes of branching random walks and implies that the critical branching random walk is transient resp.. dies
