Related papers: Random Functions via Dyson Brownian Motion: Progre…
Brownian motion in one or more dimensions is extensively used as a stochastic process to model natural and engineering signals, as well as financial data. Most works dealing with multidimensional Brownian motion consider the different…
The geometry of the multifractional Brownian motion (mBm) is known to present a complex and surprising form when the Hurst function is greatly irregular. Nevertheless, most of the literature devoted to the subject considers sufficiently…
This paper presents a new method for modelling the dynamic behaviour of developable ribbons, two dimensional strips with much smaller width than length. Instead of approximating such surface with a general triangle mesh, we characterize it…
Excursion reflected Brownian motion (ERBM) is a strong Markov process defined in a finitely connected domain $D \subset \mathbb{C}$ that behaves like a Brownian motion away from the boundary of $D$ and picks a point according to harmonic…
We study scalar perturbations to a Robertson-Walker cosmological metric in terms of a pseudo-Newtonian potential, which emerges naturally from the solution of the field equations. This potential is given in terms of a Green function for…
Under certain mild conditions, some limit theorems for functionals of two independent Gaussian processes are obtained. The results apply to general Gaussian processes including fractional Brownian motion, sub-fractional Brownian motion and…
Fractional Brownian motion is a Gaussian stochastic process with long-range correlations in time; it has been shown to be a useful model of anomalous diffusion. Here, we investigate the effects of mutual interactions in an ensemble of…
Resource allocation plays a central role in many networked systems such as smart grids, communication networks and urban transportation systems. In these systems, many constraints have physical meaning and having feasible allocation is…
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…
We introduce and study a model in one dimension of $N$ run-and-tumble particles (RTP) which repel each other logarithmically in the presence of an external quadratic potential. This is an "active'' version of the well-known Dyson Brownian…
In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some…
Dyson's Brownian motion model with the parameter $\beta=2$, which we simply call the Dyson model in the present paper, is realized as an $h$-transform of the absorbing Brownian motion in a Weyl chamber of type A. Depending on initial…
The fractional Brownian motion (fBm) is a paradigmatic strongly non-Markovian process with broad applications in various fields. Despite their importance, the properties of the territory covered by a $d$-dimensional fBm have remained…
Numerical algorithms are proposed for simulating the Brownian dynamics of charged particles in an external magnetic field, taking into account the Brownian motion of charged particles, damping effect and the effect of magnetic field…
Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…
Brownian motion with darning (BMD in abbreviation) is introduced and studied in [4] and [5, Chapter 7]. Roughly speaking, BMD travels across the "darning area" at infinite speed, while it behaves like a regular BM outside of this area. In…
We introduce a variation of the step-reinforced random walk with general memory. For the diffusive regime, we establish a functional invariance principle and show that, given suitable conditions on the memory sequence, the arising limiting…
Robot motion planning is central to real-world autonomous applications, such as self-driving cars, persistence surveillance, and robotic arm manipulation. One challenge in motion planning is generating control signals for nonlinear systems…
We propose a new algorithm to generate a fractional Brownian motion, with a given Hurst parameter, 1/2<H<1 using the correlated Bernoulli random variables with parameter p; having a certain density. This density is constructed using the…
This paper develops the first method for the exact simulation of reflected Brownian motion (RBM) with non-stationary drift and infinitesimal variance. The running time of generating exact samples of non-stationary RBM at any time $t$ is…