Related papers: Brownian Motion with a Singular Drift
The passage of Brownian motion through a bottleneck in a bounded domain is a rare event and the mean time for such passage increases indefinitely as the bottleneck's radius shrinks to zero. Its calculation reveals the effect of geometry and…
We study the order-disorder transition in colloidal suspensions under shear flow by performing Brownian dynamics simulations. We characterize the transition in terms of a statistical property of time-dependent maximum value of the structure…
Brownian motion of single particles with various masses M and diameters D is studied by molecular dynamics simulations. Besides the momentum auto-correlation function of the Brownian particle the memory function and the fluctuating force…
We show the linear drift of the Brownian motion on the universal cover of a closed connected Riemannian manifold is $C^{k-2}$ differentiable along any $C^{k}$ curve in the manifold of $C^k$ metrics with negative sectional curvature. We also…
Classical arcsine law states that fraction of occupation time on the positive or the negative side in Brownian motion does not converge to a constant but converges in distribution to the arcsine distribution. Here, we consider how a…
We derive integral formulas, involving the Airy function, for moments of the time a two-sided Brownian motion with parabolic drift attains its maximum.
An ordinary differential equation perturbed by a null-recurrent diffusion will be considered in the case where the averaging type perturbation is strong only when a fast motion is close to the origin. The normal deviations of these…
This paper studies Brownian motion subject to the occurrence of a minimal length excursion below a given excursion level. The law of this process is determined. The characterization is explicit and shows by a layer construction how the law…
We introduce a natural family of random walks on the set of integers that scale to fractional Brownian motion. The increments X_n have the property that given {X_k: k < n}, the conditional law of X_n is that of X_{n-k_n}, where k_n is…
We consider the last zero crossing time $T_{\mu,t}$ of a Brownian motion, with drift $\mu \neq 0$ in the time interval $[0, t]$. We prove the large deviation principle of $\{T_{\mu \sqrt r t} : r > 0 \}$ as $r$ tends to infinity. Moreover,…
This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated…
We study questions of existence and uniqueness of weak and strong solutions for a one-sided Tanaka equation with constant drift \lambda. We observe a dichotomy in terms of the values of the drift parameter: for \lambda\leq 0, there exists a…
A theoretical parallel between the classical Brownian motion and quantum mechanics is explored. It is shown that, in contrast to the classical Langevin force, quantum mechanics is driven by turbulent velocity fluctuations with diffusive…
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the…
We study the motion of a random walker in one longitudinal and d transverse dimensions with a quenched power law correlated velocity field in the longitudinal x-direction. The model is a modification of the Matheron-de Marsily (MdM) model,…
The dynamical friction and diffusion coefficients are derived for a massive binary that moves against a uniform background of stars. The random impulses exerted on the binary's center of mass by the field stars are greater than those…
The area swept out under a one-dimensional Brownian motion till its first-passage time is analysed using a backward Fokker-Planck technique. We obtain an exact expression of the area distribution for the zero drift case, and provide various…
In this note we introduce and solve a soft classification version of the famous Bayesian sequential testing problem for a Brownian motion's drift. We establish that the value function is the unique non-trivial solution to a free boundary…
Combining experiments on active colloids, whose propulsion velocity can be controlled via a feedback loop, and theory of active Brownian motion, we explore the dynamics of an overdamped active particle with a motility that depends…
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…