arXiv subjects

Jürgen Angst

Publications and source records attributed to Jürgen Angst.

21 records · Page 2Linked to original sources

arXiv2013

Dévissage of a Poisson boundary under equivariance and regularity conditions

We present a method that allows, under suitable equivariance and regularity conditions, to determine the Poisson boundary of a diffusion starting from the Poisson boundary of a sub-diffusion of the original one. We then give two examples of application of this dévissage method. Namely, we first recover the classical result that the Poisson boundary of Brownian motion on a rotationally symmetric manifolds is generated by its escape angle, and we then give an "elementary" probabilistic proof of the delicate result of [Bai08], i.e. the determination of the Poisson boundary of the relativistic Brownian motion in Minkowski space-time.

math.PR↗

arXiv2011

Trends to equilibrium for a class of relativistic diffusions

We address the question of the trends to equilibrium for a large class C of relativistic diffusions. We show the existence of a spectral gap using the Lyapounov method and deduce the exponential decay of the distance to equilibrium in L2-norm and in total variation. A similar result was obtained recently in arXiv:1009.5086 for a particular process of the class C.

math.PR↗

arXiv2007

Central Limit Theorem for a Class of Relativistic Diffusions

Two similar Minkowskian diffusions have been considered, on one hand by Barbachoux, Debbasch, Malik and Rivet ([BDR1], [BDR2], [BDR3], [DMR], [DR]), and on the other hand by Dunkel and Hänggi ([DH1], [DH2]). We address here two questions, asked in [DR] and in ([DH1], [DH2]) respectively, about the asymptotic behaviour of such diffusions. More generally, we establish a central limit theorem for a class of Minkowskian diffusions, to which the two above ones belong. As a consequence, we correct a partially wrong guess in [DH1].

math.PR↗