arXiv subjects
Publications and source records attributed to Yasuhito Nishimori.
We study the growth order of the maximal displacement of branching symmetric $α$-stable processes. We assume the branching rate measure $μ$ is in the Kato class and $μ$ has a compact support on ${\mathbb R}^d$. We show that the maximal displacement exponentially grows and its order is determined by the index $α$ and the spectral bottom of the corresponding Schrödinger-type operator.
A compactness of the Revuz map is established in the sense that the locally uniform convergence of a sequence of positive continuous additive functionals is derived in terms of their smooth measures. To this end, we first introduce a metric on the space of measures of finite energy integrals and show some structures of the metric. Then, we show the compactness and give some examples of positive continuous additive functionals that the convergence holds in terms of the associated smooth measures.
Our purpose in this paper is to determine the limiting distribution and the evolution rate of particles near the frontier of branching Brownian motions. Here the branching rate is given by a Kato class measure with compact support in Euclidean space. Our investigation focuses on the two dimensional case.
We determine the long time behavior and the exact order of the tail probability for the maximal displacement of a branching Brownian motion in Euclidean space in terms of the principal eigenvalue of the associated Schrödinger type operator. To establish our results, we show a sharp and locally uniform growth order of the Feynman-Kac semigroup.