Related papers: Skew Brownian motion with dry friction: joint dens…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
Understanding and predicting the dynamical properties of systems involving dry friction is a major concern in physics and engineering. It abounds in many mechanical processes, from the sound produced by a violin to the screeching of chalk…
We study the Brownian motion of a rigid rod threading through a small fixed ring while the ring can freely rotate. We derive the distribution function for the sliding displacement and the unit vector along the rod both at equilibrium and…
Statistical properties of Brownian motion that arise by analyzing, separately, trajectories over which the system energy increases (upside) or decreases (downside) with respect to a threshold energy level, are derived. This selective…
This paper derives the non-analytic solution to the Fokker-Planck equation of fractional Brownian motion using the method of Laplace transform. Sequentially, by considering the fundamental solution of the non-analytic solution, this paper…
Area fluctuations of a Brownian excursion are described by the Airy distribution, which found applications in different areas of physics, mathematics and computer science. Here we generalize this distribution to describe the area…
We consider exponential functionals of a multi-dimensional Brownian motion with drift, defined via a collection of linear functionals. We give a characterization of the Laplace transform of their joint law as the unique bounded solution, up…
We consider the occupation area of spherical (fractional) Brownian motion, i.e. the area where the process is positive, and show that it is uniformly distributed. For the proof, we introduce a new simple combinatorial view on occupation…
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 survey existing results concerning the study in small times of the density of the solution of a rough differential equation driven by fractional Brownian motions. We also slightly improve existing results and discuss some possible…
We construct a two-dimensional diffusion process with rank-dependent local drift and dispersion coefficients, and with a full range of patterns of behavior upon collision that range from totally frictionless interaction, to elastic…
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…
We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
This paper addresses the question of how Brownian-like motion can arise from the solution of a deterministic differential delay equation. To study this we analytically study the bifurcation properties of an apparently simple differential…
The distribution of the first hitting time of a disc for the standard two dimensional Brownian motion is computed. By investigating the inversion integral of its Laplace transform we give fairy detailed asymptotic estimates of its density…
Sticky Brownian motions, as time-changed semimartingale reflecting Brownian motions, have various applications in many fields, including queuing theory and mathematical finance. In this paper, we are concerned about the stationary…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
We derive a Ray-Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken…