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We determine the space-dependent source term for a two-parameter fractional diffusion problem subject to nonlocal non-self-adjoint boundary conditions and two local time-distinct datum. A bi-orthogonal pair of bases is used to construct a…
We consider a family of hard core objects moving as independent Brownian motions confined to a vessel by reflection. These are subject to gravitational forces modeled by drifts. The stationary distribution for the process has many…
We study a one-dimensional diffusion $X$ in a drifted Brownian potential $W\_\kappa$, with $ 0\textless{}\kappa\textless{}1$, and focus on the behavior of the local times $(\mathcal{L}(t,x),x)$ of $X$ before time $t\textgreater{}0$.In…
We consider in this work a one parameter family of hypoelliptic diffusion processes on the unit tangent bundle $T^1 \mathcal M$ of a Riemannian manifold $(\mathcal M,g)$, collectively called kinetic Brownian motions, that are random…
In this paper the solutions $u_{\nu}=u_{\nu}(x,t)$ to fractional diffusion equations of order $0<\nu \leq 2$ are analyzed and interpreted as densities of the composition of various types of stochastic processes. For the fractional equations…
We investigate the dynamics of Brownian particles in internal state- dependent symmetric and periodic potentials. Although no space or time symmetry of the Hamiltonian is broken, we show that directed transport can appear. We demonstrate…
Simultaneous diffusive and inertial motion of Brownian particles in laminar Couette flow is investigated via Lagrangian and Eulerian descriptions to determine the effect of particle inertia on diffusive transport in the long-time. The…
We study the dynamics of a Brownian particle in a strongly correlated quenched random potential defined as a periodically-extended (with period $L$) finite trajectory of a fractional Brownian motion with arbitrary Hurst exponent $H \in…
We propose an approach to compute the boundary crossing probabilities for a class of diffusion processes which can be expressed as piecewise monotone (not necessarily one-to-one) functionals of a standard Brownian motion. This class…
The scaled Brownian motion (SBM) is regarded as one of the paradigmatic random processes, featuring the anomalous diffusion property characterized by the diffusion exponent. It is a Gaussian, self-similar process with independent…
In this paper, we study a particular model of distorted Brownian motion (dBM) on state spaces with varying dimension. Roughly speaking, the state space of such a process consists of two components: a $3$-dimensional component and a…
The celebrated Sutherland-Einstein relation for systems at thermal equilibrium states that spread of trajectories of Brownian particles is an increasing function of temperature. Here, we scrutinize diffusion of underdamped Brownian motion…
We study exclusion processes on the integer lattice in which particles change their velocities due to stickiness. Specifically, whenever two or more particles occupy adjacent sites, they stick together for an extended period of time, and…
We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth…
This article studies the quasi-stationary behaviour of absorbed one-dimensional diffusions. We obtain necessary and sufficient conditions for the exponential convergence to a unique quasi-stationary distribution in total variation,…
In active Brownian motion, an internal propulsion mechanism interacts with translational and rotational thermal noise and other internal fluctuations to produce directed motion. We derive the distribution of its extreme fluctuations and…
We study the long time behavior of a Brownian particle moving in an anomalously diffusing field, the evolution of which depends on the particle position. We prove that the process describing the asymptotic behaviour of the Brownian particle…
We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between a background fluid velocity and the…
We consider the motion of an active Brownian particle with speed fluctuations in d-dimensions in the presence of both translational and orientational diffusion. We use an Ornstein-Uhlenbeck process for active speed generation. Using a…
Lateral diffusion of molecules on surfaces plays a very important role in various biological processes, including lipid transport across the cell membrane, synaptic transmission and other phenomena such as exo- and endocytosis, signal…