Identification of stochastic loads applied to a nonlinear dynamical system using an uncertain computational model.
Initial data stability and admissibility of spaces for Itô linear difference equations
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 -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
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 densities of random maps have lower bounds on their supports.
Invariant jets of a smooth dynamical system
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 , a condition on the Lyapunov exponents of the dynamical system is established insuring the convergence of the -jet of...
Invariant measures for position dependent random maps with continuous random parameters
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
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.