All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 2 Next

Displaying 21 – 40 of 76

Showing per page

Ergodicity of increments of the Rosenblatt process and some consequences

Petr Čoupek, Pavel Křížek, Bohdan Maslowski (2025)

Czechoslovak Mathematical Journal

A new proof of the mixing property of the increments of Rosenblatt processes is given. The proof relies on infinite divisibility of the Rosenblatt law that allows to prove only the pointwise convergence of characteristic functions. Subsequently, the result is used to prove weak consistency of an estimator for the self-similarity parameter of a Rosenblatt process, and to prove the existence of a random attractor for a random dynamical system induced by a stochastic reaction-diffusion equation driven...

Estimates for Principal Lyapunov Exponents: A Survey

Janusz Mierczyński (2014)

Nonautonomous Dynamical Systems

This is a survey of known results on estimating the principal Lyapunov exponent of a timedependent linear differential equation possessing some monotonicity properties. Equations considered are mainly strongly cooperative systems of ordinary differential equations and parabolic partial differential equations of second order. The estimates are given either in terms of the principal (dominant) eigenvalue of some derived time-independent equation or in terms of the parameters of the equation itself....

Exponential convergence to the stationary measure and hyperbolicity of the minimisers for random Lagrangian Systems

Boritchev, Alexandre (2017)

Proceedings of Equadiff 14

We consider a class of 1d Lagrangian systems with random forcing in the spaceperiodic setting: φ t + φ x 2 / 2 = F ω , x ∈ S 1 = ℝ / ℤ . These systems have been studied since the 1990s by Khanin, Sinai and their collaborators [7, 9, 11, 12, 15]. Here we give an overview of their results and then we expose our recent proof of the exponential convergence to the stationary measure [6]. This is the first such result in a classical setting, i.e. in the dual-Lipschitz metric with respect to the Lebesgue space L p for finite p , partially answering...

Geometry of non-holonomic diffusion

Simon Hochgerner, Tudor S. Ratiu (2015)

Journal of the European Mathematical Society

We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For G -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.

Initial data stability and admissibility of spaces for Itô linear difference equations

Ramazan Kadiev, Pyotr Simonov (2017)

Mathematica Bohemica

The admissibility of spaces for Itô functional difference equations is investigated by the method of modeling equations. The problem of space admissibility is closely connected with the initial data stability problem of solutions for Itô delay differential equations. For these equations the p -stability of initial data solutions is studied as a special case of admissibility of spaces for the corresponding Itô functional difference equation. In most cases, this approach seems to be more constructive...

Intermittency properties in a hyperbolic Anderson problem

Robert C. Dalang, Carl Mueller (2009)

Annales de l'I.H.P. Probabilités et statistiques

We study the asymptotics of the even moments of solutions to a stochastic wave equation in spatial dimension 3 with linear multiplicative spatially homogeneous gaussian noise that is white in time. Our main theorem states that these moments grow more quickly than one might expect. This phenomenon is well known for parabolic stochastic partial differential equations, under the name of intermittency. Our results seem to be the first example of this phenomenon for hyperbolic equations. For comparison,...

Invariant jets of a smooth dynamical system

Sophie Lemaire (2001)

Bulletin de la Société Mathématique de France

The local deformations of a submanifold under the effect of a smooth dynamical system are studied with the help of Oseledets’ multiplicative ergodic theorem. Equivalence classes of submanifolds, called jets, are introduced in order to describe these local deformations. They identify submanifolds having the same approximations up to some order at a given point. For every order k , a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the k -jet of...

Invariant measures for position dependent random maps with continuous random parameters

Tomoki Inoue (2012)

Studia Mathematica

We consider a family of transformations with a random parameter and study a random dynamical system in which one transformation is randomly selected from the family and applied on each iteration. The parameter space may be of cardinality continuum. Further, the selection of the transformation need not be independent of the position in the state space. We show the existence of absolutely continuous invariant measures for random maps on an interval under some conditions.

Isomorphic random Bernoulli shifts

V. Gundlach, G. Ochs (2000)

Colloquium Mathematicae

We develop a relative isomorphism theory for random Bernoulli shifts by showing that any random Bernoulli shifts are relatively isomorphic if and only if they have the same fibre entropy. This allows the identification of random Bernoulli shifts with standard Bernoulli shifts.

Currently displaying 21 – 40 of 76