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5 papers · 2 filters
Quasi-stochastic matrices and Markov renewal theory
Gerold Alsmeyer
Given a matrix of distribution functions and a quasi-stochastic matrix, i.e. an irreducible nonnegative matrix with maximal eigenvalue one and associated unique positive left and r…
The scaling limit of the interface of the continuous-space symbiotic branching model
Jochen Blath, Matthias Hammer, Marcel Ortgiese
The continuous-space symbiotic branching model describes the evolution of two interacting populations that can reproduce locally only in the simultaneous presence of each other. If…
Local Lipschitz continuity in the initial value and strong completeness for nonlinear stochastic differential equations
Sonja Cox, Martin Hutzenthaler, Arnulf Jentzen
Recently, Hairer et. al (2012) showed that there exist SDEs with infinitely often differentiable and globally bounded coefficient functions whose solutions fail to be locally Lipsc…
Robust analysis of preferential attachment models with fitness
Steffen Dereich, Marcel Ortgiese
The preferential attachment network with fitness is a dynamic random graph model. New vertices are introduced consecutively and a new vertex is attached to an old vertex with proba…
On Kesten's Multivariate Choquet-Deny Lemma
Sebastian Mentemeier
Let and be a sequence of independent identically distributed random matrices with nonnegative entries and no zero column. This induces a Markov chain $M_n…