Related papers: Skew Brownian motion with dry friction: joint dens…
We study the distribution of additive functionals of reset Brownian motion, a variation of normal Brownian motion in which the path is interrupted at a given rate and placed back to a given reset position. Our goal is two-fold: (1) For…
For drifted Brownian motion $X(t)= x - \mu t + B_t \ (\mu >0)$ starting from $x>0,$ we study the joint distribution of the first-passage time below zero, $\tau(x),$ and the first-passage area, $A(x),$ swept out by $X$ till the time…
We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…
The existence of two types of internal friction wet and dry is revisited, and a simple protocol is proposed for distinguishing between the two types and extracting the appropriate internal friction coefficient. The scheme requires…
We study the relation between flow structure and fluid deformation in steady two-dimensional random flows. Beyond the linear (shear flow) and exponential (chaotic flow) elongation paradigms, we find a broad spectrum of stretching behaviors,…
A stochastic leap-frog algorithm for the numerical integration of Brownian motion stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time…
We consider the solid or hexatic non-equilibrium phases of an interacting two-dimensional system of Active Brownian Particles at high density and investigate numerically and theoretically the properties of the velocity distribution function…
We study a Langevin equation describing the Brownian motion of an object subjected to a viscous drag, an external constant force, and a solid friction force of the Coulomb type. In a previous work [H. Touchette, E. Van der Straeten, W.…
In this paper, we obtain analytical expression for the distribution of the occupation time in the red (below level $0$) up to an (independent) exponential horizon for spectrally negative L\'{e}vy risk processes and refracted spectrally…
We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…
We consider a refracted jump diffusion process having two-sided jumps with rational Laplace transforms. For such a process, by applying a straightforward but interesting approach, we derive formulas for the Laplace transform of its…
We consider a Brownian motion with drift in the quarter plane with orthogonal reflection on the axes. The Laplace transform of its stationary distribution satisfies a functional equation, which is reminiscent from equations arising in the…
We provide a general model for Brownian motions on metric graphs with interactions. In a general setting, for (sticky) Brownian propagations on edges, our model provides a characterization of lifetimes and holding times on vertices in terms…
The seismically active regions often correlate with fault lines, and the movement of these faults plays a crucial role in defining how stress is stored or released in these areas. To investigate the deformation and accumulation/release of…
The comparison theorem for skew Brownian motions is proved. As the corollary we get the estimate on ${\Cal L}_1-$distance between two skew Brownian motions started from different points. Using this result we prove the continuous dependence…
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 describe a test particle approach based on dynamical density functional theory (DDFT) for studying the correlated time evolution of the particles that constitute a fluid. Our theory provides a means of calculating the van Hove…
We study the local time distribution of a Brownian particle diffusing along the links on a graph. In particular, we derive an analytic expression of its Laplace transform in terms of the Green's function on the graph. We show 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…
We study structural relaxation of colloidal hard spheres undergoing Brownian motion using dynamical density functional theory. Contrary to the partial linearization route [Stopper {\em et al.}, Phys. Rev. E {\bf 92}, 022151 (2015)] which…