Related papers: Langevin process reflected on a partially elastic …
In this paper we study macroscopic density equations in which the diffusion coefficient depends on a weighted spatial average of the density itself. We show that large differences (not present in the local density-dependence case) appear…
On the base of a 1D Shr\"{o}dinger equation the non-linear first-order differential equation (Ricatti type) for a quantum wave impedance function was derived. The advantages of this approach were discussed and demonstrated for a case of a…
The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation…
Response lags are generic to almost any physical system and often play a crucial role in the feedback loops present in artificial nanodevices and biological molecular machines. In this paper, we perform a comprehensive study of small…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
We consider a diffusion process with coefficients that are periodic outside of an "interface region" of finite thickness. The question investigated in this article is the limiting long time/large scale behavior of such a process under…
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…
Two frameworks that have been used to characterize reflected diffusions include stochastic differential equations with reflection and the so-called submartingale problem. We introduce a general formulation of the submartingale problem for…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
We investigate the influence of a self-propelling, out-of-equilibrium active particle on generalized elastic systems, including flexible and semiflexible polymers, fluid membranes, and fluctuating interfaces, while accounting for…
We consider a random walk on the first quadrant of the square lattice, whose increment law is, roughly speaking, homogeneous along a finite number of half-lines near each of the two boundaries, and hence essentially specified by…
In this paper, we investigate the recovery of the absorption coefficient from boundary data assuming that the region of interest is illuminated at an initial time. We consider a sufficiently strong and isotropic, but otherwise unknown…
The Langevin equation (LE) for the one-dimensional relativistic Brownian motion is derived from a microscopic collision model. The model assumes that a heavy point-like Brownian particle interacts with the lighter heat bath particles via…
We prove regenerative properties for the linear Hawkes process under minimal assumptions on the transfer function, which may have unbounded support. These results are applicable to sliding window statistical estimators. We exploit…
In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson…
We consider a jump-diffusion process on a bounded domain with reflection at the boundary, and establish long-term results for a general additive process of its path. This includes the long-term behaviour of its occupation time in the…
Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic…
We consider a stochastic partial differential equation with logarithmic (or negative power) nonlinearity, with one reflection at 0 and with a constraint of conservation of the space average. The equation, driven by the derivative in space…
Assuming that a reflected Ornstein-Uhlenbeck state process is observed at discrete time instants, we propose generalized moment estimators to estimate all drift and diffusion parameters via the celebrated ergodic theorem. With the sampling…
In this work, we study nonlocal differential equations with particular focus on those with reflection in their argument and piecewise constant dependence. The approach entails deriving the explicit expression of the solution to the linear…