6 papers
Persistence of autoregressive sequences with logarithmic tails
Denis Denisov, Gunter Hinrich, Martin Kolb +1
We consider autoregressive sequences and with a constant and with positive, independent and identically distributed innova…
Spectral Asymptotics for Kinetic Brownian Motion on Hyperbolic Surfaces
Martin Kolb, Tobias Weich, Lasse Lennart Wolf
The kinetic Brownian motion on the sphere bundle of a Riemannian manifold is a stochastic process that models a random perturbation of the geodesic flow. If is a orientable…
A Characterization of the Finiteness of Perpetual Integrals of Levy Processes
Martin Kolb, Mladen Savov
We derive a criterium for the almost sure finiteness of perpetual integrals of \LL processes for a class of real functions including all continuous functions and for general one-di…
Stochastic spikes and Poisson Approximation of one-dimensional stochastic differential equations with applications to continuously measured Quantum Systems
Martin Kolb, Matthias Liesenfeld
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting p…
On the Spectral Gap of Brownian Motion with Jump Boundary
Martin Kolb, Achim Wübker
In this paper we consider the Brownian motion with jump boundary and present a new proof of a recent result of Li, Leung and Rakesh concerning the exact convergence rate in the one…
Spectral Analysis of Diffusions with Jump Boundary
Martin Kolb, Achim Wübker
In this paper we consider one-dimensional diffusions with constant coefficients in a finite interval with jump boundary and a certain deterministic jump distribution. We use coupli…