Related papers: Random motions in $\mathbb{R}^3$ with orthogonal d…
The symmetric top is a special case of the general top, and canonical Poisson structure on $T^*SE(3)$ is the common method of its description. This structure is invariant under the right action of $SO(3)$, but the Hamiltonian of the…
The flashing Brownian ratchet is a stochastic process that alternates between two regimes, a one-dimensional Brownian motion and a Brownian ratchet, the latter being a one-dimensional diffusion process that drifts towards a minimum of a…
In this paper we introduce a general stochastic representation for an important class of processes with resetting. It allows to describe any stochastic process intermittently terminated and restarted from a predefined random or non-random…
We experimentally demonstrate the emergence of directional rotation in thermally active-passive colloidal structures under optical confinement. The observed handedness of rotation of the structure can be controlled by changing the relative…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
We prove convex ordering results for random vectors admitting a predictable representation in terms of a Brownian motion and a non-necessarily independent jump component. Our method uses forward-backward stochastic calculus and extends…
In the article random functions in modules over the octonion algebra and Cayley-Dickson algebras are investigated. For their study transition measures with values in the octonion algebra and Cayley-Dickson algebras are used. Stochastic…
In this paper, we introduce a family of discrete rectangular uniform distributions on the natural numbers-referred to as orthogonal dice-characterized by the property that their means equal their variances. These distributions arise…
We study the distribution of the positive sojourn time $$ A_t:= \int_0^t \mathbf 1\{ X_s>0 \}ds $$ of an arbitrary L\'evy process $X:= (X_t)_{t\geq 0}$. For an exponential random variable $E^{(q)}$ of rate $q>0$ independent of $X$ we show…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
We consider a discrete random walk on a diagonal lattice in two and three dimensions and obtain explicit solutions of absorption probabilities and probabilities of return in several domains. In three dimensions we consider both the cube and…
We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space. Generalizing the zero cell of such a process, we fix a convex body $K$ and consider the intersection…
Many astrophysical phenomena are time-varying, in the sense that their intensity, energy spectrum, and/or the spatial distribution of the emission suddenly change. This paper develops a method for modeling a time series of images. Under the…
This is the first part of a threefold article, aimed at solving numerically the Poisson problem in three-dimensional prismatic or axisymmetric domains. In this first part, the Fourier Singular Complement Method is introduced and analysed,…
In this paper, we determine the Poisson boundary of the relativistic Brownian motion in two classes of Lorentzian manifolds, namely model manifolds of constant scalar curvature and Robertson--Walker space-times, the latter constituting a…
The topological orders in amorphous systems that lack crystalline symmetry have gained considerable attention recently. Here we propose the Floquet amorphous topological matter, among which the topological orders are explored in…
Stationary Poisson processes of lines in the plane are studied whose directional distributions are concentrated on $k \ge 3$ equally spread directions. The random lines of such processes decompose the plane into a collection of random…
The three-body problem is a fundamental long-standing open problem, with applications in all branches of physics, including astrophysics, nuclear physics and particle physics. In general, conserved quantities allow to reduce the formulation…
The Poisson boundary of a finite direct product of affine automorphism groups of homogeneous trees is considered. The Poisson boundary is shown to be a product of ends of trees with a hitting measure for spread-out, aperiodic measures of…