43 citations · 79 across the 17 of their papers we have counts for
12 papers · 1 filter
Brownian motion conditioned to spend limited time outside a bounded interval -- an extreme example of entropic repulsion
Frank Aurzada, Martin Kolb, Dominic T. Schickentanz
We show that a Brownian motion on which is allowed to spend a total of time units outside a bounded interval does not leave the interval at all. This c…
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…
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…
Persistence of one-dimensional AR(1)-sequences
Günter Hinrichs, Martin Kolb, Vitali Wachtel
For a class of one-dimensional autoregressive processes we consider the tail behaviour of the stopping time . We discuss existi…
Quasistationary distributions for one-dimensional diffusions with singular boundary points
Alexandru Hening, Martin Kolb
In the present work we characterize the existence of quasistationary distributions for diffusions on allowing singular behavior at and . If absorption at 0…
Conditional survival distributions of Brownian trajectories in a one dimensional Poissonian environment in the critical case
Martin Kolb, Mladen Savov
In this work we consider a one-dimensional Brownian motion with constant drift moving among a Poissonian cloud of obstacles. Our main result proves convergence of the law of proces…
Transience and recurrence of a Brownian path with limited local time and its repulsion envelope
Martin Kolb, Mladen Savov
In this note we investigate the behaviour of Brownian motion conditioned on a growth constraint of its local time which has been previously investigated by Berestycki and Benjamini…
The rate of convergence to stationarity for M/G/1 models with admission controls via coupling
Martin Kolb, Wolfgang Stadje, Achim Wübker
We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2…
Geometric Ergodicity of a Hypoelliptic Diffusion Modelling The Melt-Spinning Process of Nonwoven Materials
Martin Kolb, Mladen Savov, Achim Wubker
We analyze the large time behavior of a stochastic model for the lay-down of fibers on a conveyor belt in the production process of nonwovens. It is shown, that under weak conditio…
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…
Quasilimiting behavior for one-dimensional diffusions with killing
Martin Kolb, David Steinsaltz
This paper extends and clarifies results of Steinsaltz and Evans [Trans. Amer. Math. Soc. 359 (2007) 1285-1234], which found conditions for convergence of a killed one-dimensional…