相关论文: Annealed Brownian motion in a heavy tailed Poisson…
We consider the Feynman-Kac functional associated with a Brownian motion in a random potential. The potential is defined by attaching a heavy tailed positive potential around the Poisson point process. This model was first considered by…
We consider the parabolic Anderson problem with random potentials having inverse-square singularities around the points of a standard Poisson point process in $\mathbb{R}^d$, $d \geq 3$. The potentials we consider are obtained via…
Motivated by the study of the directed polymer model with mobile Poissonian traps or catalysts and the stochastic parabolic Anderson model with time dependent potential, we investigate the asymptotic behavior of…
We study Brownian motion in a drifted Brownian potential in the subexponential regime. We prove that the annealed probability of deviating below the almost sure speed has a polynomial rate of decay and compute the exponent in this power…
We study trajectories of d-dimensional Brownian Motion in Poissonian potential up to the hitting time of a distant hyper-plane. Our Poissonian potential V can be associated to a field of traps whose centers location is given by a Poisson…
We analyze the existence of Brownian motion tilted by a potential of full support on hyperbolic spaces $\mathbb{H}^d$. On compact spaces, it is classical that these path limits, called Q-processes, exist and can be directly defined using…
We study the one-dimensional motion of a Brownian particle inside a confinement described by two reactive boundaries which can partially reflect or absorb the particle. Understanding the effects of such boundaries is important in physics,…
We investigate the transport of Brownian particles in a two-dimensional potential under the action of a uniform external force. The potential is periodic in one direction and confines the particle to a narrow channel of varying…
We analyze the Brownian Motion limit of a prototypical unit step reinforced random-walk on the half line. A reinforced random walk is one which changes the weight of any edge (or vertex) visited to increase the frequency of return visits.…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
In this paper, we determine the Poisson boundary of the relativistic Brownian motion in two classes of Lorentzian manifolds, namely model manifolds of constant scalar curvature and Robertson--Walker space-times, the latter constituting a…
We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$,…
We show how from an unique standard Poisson process we can build a family of processes that converges in law to a $d$-dimensional standard Brownian motion for any $d \ge 1$.
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
We describe generalized Brownian motion related to parabolic equation systems from a logical point of view, i.e., as a generalization of Anderson's random walk. The connection to classical spaces is based on the Loeb measure. It seems that…
Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these…
Based on analytical and numerical calculations we study the dynamics of an overdamped colloidal particle moving in two dimensions under time-delayed, non-linear feedback control. Specifically, the particle is subject to a force derived from…
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical…
Brownian motion near soft surfaces is a situation widely encountered in nanoscale and biological physics. However, a complete theoretical description is lacking to date. Here, we theoretically investigate the dynamics of a two-dimensional…
Barrier crossing is a widespread phenomenon across natural and engineering systems. While an abundant cross-disciplinary literature on the topic has emerged over the years, the stochastic underpinnings of the process are yet to be linked…