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Within a high-frequency framework, we propose a non-parametric approach to estimate a family of copulas associated to a time-changed Brownian motion. We show that our estimator is consistent and asymptotically mixed-Gaussian. Furthermore,…
A new framework to perturbative quantum gravity is proposed following the geometry of nonholonomic distributions on (pseudo) Riemannian manifolds. There are considered such distributions and adapted connections, also completely defined by a…
For $N$-coupled generalized time-dependent oscillators, primary invariants and a generalized invariant are found in terms of classical solutions. Exact quantum motions satisfying the Heisenberg equation of motion are also found. For number…
We show that tensoriality constraints in noncommutative Riemannian geometry in the 2-dimensional bicrossproduct model quantum spacetime algebra [x,t]=\lambda x drastically reduce the moduli of possible metrics g up to normalisation to a…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
In this article, we propose a control law for almost-global asymptotic tracking (AGAT) of a smooth reference trajectory for a fully actuated simple mechanical system (SMS) evolving on a Riemannian manifold which can be embedded in a…
We study a space-time Brownian motion with drift B(t)=(t_0+t,y_0+W(t)+t) killed at the moving boundary of the cone {(t,x):0<x<t}. This article determines the parabolic Martin boundary and all harmonic functions associated with this process.…
We present a numerical implementation of the renormalization group (RG) for partial differential equations, constructing similarity solutions and travelling waves. We show that for a large class of well-localized initial conditions,…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
Presented is description of kinematics and dynamics of material points with internal degrees of freedom moving in a Riemannian manifold. The models of internal degrees of freedom we concentrate on are based on the orthogonal and affine…
We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed…
Parametric manifold optimization problems frequently arise in various machine learning tasks, where state functions are defined on infinite-dimensional manifolds. We propose a unified accelerated natural gradient descent (ANGD) framework to…
The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and…
We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description…
A model of self-driven particles similar to the Vicsek model [Phys. Rev. Lett. 75 (1995) 1226] but with metric-free interactions is studied by means of a novel Enskog-type kinetic theory. In this model, N particles of constant speed v0 try…
In this paper, we will present a strong (or pathwise) approximation of standard Brownian motion by a class of orthogonal polynomials. The coefficients that are obtained from the expansion of Brownian motion in this polynomial basis are…
We obtain Fisher-Hartwig asymptotics with root and jump type singularities in space-time under the law of the stationary Hermitian Ornstein-Uhlenbeck process, which serve as a dynamical generalization of earlier static results obtained by…
We study random "perturbation" to the geodesic equation. The geodesic equation is identified with a canonical differential equation on the orthonormal frame bundle driven by a horizontal vector field of norm $1$. We prove that the…
The asymptotic scheme of post-Newtonian approximation defined for general relativity (GR) in the harmonic gauge by Futamase & Schutz (1983) is based on a family of initial data for the matter fields of a perfect fluid and for the initial…
We consider a model of Branching Brownian Motion in which the usual spatially-homogeneous and catalytic branching at a single point are simultaneously present. We establish the almost sure growth rates of population in certain…