43 citations · 79 across the 17 of their papers we have counts for
22 papers
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…
Spectral Asymptotics for Kinetic Brownian Motion on Surfaces of Constant Curvature
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…
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…
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…
Theoretical properties of quasi-stationary Monte Carlo methods
Andi Q. Wang, Martin Kolb, Gareth O. Roberts +1
This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting dis…
Spectral analysis of the diffusion operator with random jumps from the boundary
Martin Kolb, David Krejcirik
Using an operator-theoretic framework in a Hilbert-space setting, we perform a detailed spectral analysis of the one-dimensional Laplacian in a bounded interval, subject to specifi…
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…
On the Dipole Approximation with Error Estimates
Lea Boßmann, Robert Grummt, Martin Kolb
The dipole approximation is employed to describe interactions between atoms and radiation. It essentially consists of neglecting the spatial variation of the external field over th…
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…
The Brownian traveller on manifolds
Martin Kolb, David Krejcirik
We study the influence of the intrinsic curvature on the large time behaviour of the heat equation in a tubular neighbourhood of an unbounded geodesic in a two-dimensional Riemanni…
On a stochastic Trotter formula with application to spontaneous localization models
Detlef Dürr, Günter Hinrichs, Martin Kolb
We consider the relation between so called continuous localization models - i.e. non-linear stochastic Schrödinger evolutions - and the discrete GRW-model of wave function collapse…
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…
On the Quantum Mechanical Scattering Statistics of Many Particles
Detlef Dürr, Martin Kolb, Tilo Moser +1
The probability of a quantum particle being detected in a given solid angle is determined by the -matrix. The explanation of this fact in time dependent scattering theory is oft…
On the long time behavior of stochastic Schroedinger evolutions
Angelo Bassi, Detlef Duerr, Martin Kolb
We discuss the time evolution of the wave function which is solution of a stochastic Schroedinger equation describing the dynamics of a free quantum particle subject to spontaneous…