Nonconventional limit theorems in averaging

Abstract

We consider "nonconventional" averaging setup in the form $\frac{d{X}^{\epsilon }(t)}{dt}=\epsilon B(X^{\epsilon }(t),\xi (q_1(t)),\xi (q_2(t)),...,\xi (q_{\ell }(t)))$ where $\xi (t),t\ge 0$ is either a stochastic process or a dynamical system (i.e. then $\xi (t)=F^{t}x$) with sufficiently fast mixing while $q_j(t)=\al_jt,\,\al_1<\al_2<...<\al_k$ and $q_j,j=k+1,...,\ell$ grow faster than linearly. We show that the properly normalized error term in the "nonconventional" averaging principle is asymptotically Gaussian.

References in corpus (2)

• Energy transfer in a fast-slow Hamiltonian system
• Central Limit Theorems in Deterministic Systems