Related papers: Area Distribution of Elastic Brownian Motion
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…
In this paper, we consider a multidimensional ergodic diffusion with jumps driven by a Brownian motion and a Poisson random measure associated with a pure-jump L\'evy process with finite L\'evy measure, whose drift coefficient depends on an…
The traction on the surface of a spherical active colloid in a thermally fluctuating Stokesian fluid contains passive, active, and Brownian contributions. Here we derive these three parts systematically, by "projecting out" the fluid using…
We provide a deep connection between elastic drifted Brownian motions and inverses to tempered subordinators. Based on this connection, we establish a link between multiplicative functionals and dynamical boundary conditions given in terms…
We investigate to what extent one can use a thermodynamic description of turbulent flow as a source of stochastic kinetic energy for three-dimensional self-assembly of magnetically interacting macroscopic particles. We confirm that the…
We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto…
In this work we develop and apply a path integral formulation for the microscopic degrees of freedom obeying stochastic differential equations to an active Brownian particle (ABP) trapped in a harmonic potential. The formalism allows to…
We consider the problem of efficient estimation for the drift of fractional Brownian motion $B^H:=(B^H_t)_{t\in[0,T]}$ with hurst parameter $H$ less than 1/2. We also construct superefficient James-Stein type estimators which dominate,…
We study the large time behavior of the optimal transportation cost towards the uniform distribution, for the occupation measure of a stationary Brownian motion on the flat torus in $d$ dimensions, where the cost of transporting a unit of…
The stochastic trajectories of molecules in living cells, as well as the dynamics in many other complex systems, often exhibit memory in their path over long periods of time. In addition, these systems can show dynamic heterogeneities due…
In this short note we derive a closed form for the trivariate distribution (position, local time at the origin, and positive occupation time) of the one-dimensional sticky Brownian motion, thereby filling some gaps and fixing some mistakes…
Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the…
The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A…
We consider an infinite system of Brownian motions which interact through a given Brownian motion being reflected from its left neighbor. Earlier we studied this system for deterministic periodic initial configurations. In this contribution…
In this work animations of the random walk movement using a freeware Algodoo were done in order to support teaching the concepts of Brownian Motion. The random walk movement were simulate considering elastic collision between the particles…
Using quantum parallelism on random walks as original seed, we introduce new quantum stochastic processes, the open quantum Brownian motions. They describe the behaviors of quantum walkers -- with internal degrees of freedom which serve as…
In this paper, we consider a two-dimensional sticky Brownian motion. Sticky Brownian motions can be viewed as time-changed semimartingale reflecting Brownian motions, which find applications in many areas including queueing theory and…
We study the Brownian motion of a charged test particle coupled to electromagnetic vacuum fluctuations near a perfectly reflecting plane boundary. The presence of the boundary modifies the quantum fluctuations of the electric field, which…
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…
Quantum Brownian motion in the strong friction limit is studied based on the exact path integral formulation of dissipative systems. In this limit the time-nonlocal reduced dynamics can be cast into an effective equation of motion, the…