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Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…
This article reports the modeling of inertial rotational Brownian motion as an Ornstein-Uhlenbeck process evolving on the cotangent bundle of the rotation group, SO(3). The benefit of this approach and the use of a different…
The main results in this paper concern large and moderate deviations for the radial component of a $n$-dimensional hyperbolic Brownian motion (for $n\geq 2$) on the Poincar\'{e} half-space. We also investigate the asymptotic behavior of the…
Let $T^D$ denote the first exit time of a planar Brownian motion from a domain $D$. Given two simply connected planar domains $U,W \neq \SC$ containing $0$, we investigate the cases in which we are more likely to have fast exits (meaning…
Consider the radial projection onto the unit sphere of the path a d-dimensional Brownian motion W, started at the center of the sphere and run for unit time. Given the occupation measure mu of this projected path, what can be said about the…
We describe the size of the sets of sojourn times $E_\gamma =\{t\geq 0: |B_t|\leq t^\gamma\}$ associated with a fractional Brownian motion $B$ in terms of various large scale dimensions.
The conventional equations of Brownian motion can be derived from the first principles to order $\lambda^2=m/M$, where $m$ and $M$ are the masses of a bath molecule and a Brownian particle respectively. We discuss the extension to order…
In this paper, we present several path properties, simulations, inferences, and generalizations of the weighted sub-fractional Brownian motion. A primary focus is on the derivation of the covariance function $R_{f,b}(s,t)$ for the weighted…
For $0<\alpha \leq 2$ and $0<H<1$, an $\alpha$-time fractional Brownian motion is an iterated process $Z = \{Z(t)=W(Y(t)), t \ge 0\}$ obtained by taking a fractional Brownian motion $\{W(t), t\in \RR{R} \}$ with Hurst index $0<H<1$ and…
We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the…
We consider matrices whose elements enumerate weights of walks in planar directed weighted graphs (not necessarily acyclic). These matrices are totally nonnegative; more precisely, all their minors are formal power series in edge weights…
An exact formula is derived, as an integral, for the mean square winding angle of Brownian motion (that is, diffusion) after time t, around an infinitely long impenetrable cylinder of radius a, having started at radius R(>a) from the axis.…
Lower and upper estimates are given for the probability that the epsilon-enlargement of planar Brownian motion to time 1 (the epsilon sausage) contains a unit line segment. The estimates imply that Brownian motion to time 1 itself contains…
We consider a random walker on a ring, subjected to resetting at Poisson-distributed times to the initial position (the walker takes the shortest path along the ring to the initial position at resetting times). In the case of a Brownian…
We consider an infinite system of non overlapping globules undergoing Brownian motions in R^3. The term globules means that the objects we are dealing with are spherical, but with a radius which is random and time-dependent. The dynamics is…
We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition…
Let $B_{H}(t), t\geq [0,T], T\in(0,\infty)$ be the standard Multifractional Brownian Motion(mBm), in this contribution we are concerned with the exact asymptotics of \begin{eqnarray*} \mathbb{P}\left\{\sup_{t\in[0,T]}B_{H}(t)>u\right\}…
In this paper, it is presented the well known aspect of non linearity of internal human body structures. Similarity on the basis of the Fractional Brownian Motion from the static ones, as the geometrical fractals like the Intestine and…
A quasi-Keplerian parameterisation for the solutions of second post-Newtonian (PN) accurate equations of motion for spinning compact binaries is obtained including leading order spin-spin and next-to-leading order spin-orbit interactions.…
The stationary radial distribution, $P(\rho)$, of the random walk with the diffusion coefficient $D$, which winds with the tangential velocity $V$ around the impenetrable disc of radius $R$ for $R\gg 1$ converges to the distribution…