TIME-DEPENDENT PRINCIPLES OF INVARIANCE

Strong Invariance Principles for Dependent Random Variables

We establish strong invariance principles for sums of stationary and ergodic processes with nearly optimal bounds. Applications to linear and some nonlinear processes are discussed. Strong laws of large numbers and laws of the iterated logarithm are also obtained under easily verifiable conditions. 1. Introduction. Strong laws of large numbers (SLLN), laws of the iterated logarithm (LIL), centr...

Invariance Principles for Recursive Residuals

Strong Invariance Principles for Sequential

Rafa l Kulik of University of Sydney and Wroc law University has brought to our attention that Assumption A does not help in the proof of our Proposition 2.2, for what is really used in our method of proof is, actually, the uniform boundedness of Jτ (y) and that of its derivatives. However, ifXi = ηi (cf. Remark 2.1), then J1(y) =−φ(Φ −1(y)), and thus, we have J ′ 1(y) =−Φ −1(y), J ′′ 1 (y) = −...

Invariance Principles for Parabolic Equations with Random Coeecients Invariance Principles for Parabolic Equations with Random Coeecients

A general Hilbert-space-based stochastic averaging theory is brought forth in this note for arbitrary-order parabolic equations with (possibly long range dependent) random coeecients. We start with regularity conditions on the coeecients and Cauchy data of @ t u " (x; t) = X 0jkjj2p A k (x; t="; !)@ k x u " (x; t); u " (x; 0) = '(x) (1) which are only slightly stronger than those required to pr...

Scaling Invariance in a Time-Dependent elliptical Billiard

We study some dynamical properties of a classical time-dependent elliptical billiard. We consider periodically moving boundary and collisions between the particle and the boundary are assumed to be elastic. Our results confirm that although the static elliptical billiard is an integrable system, after to introduce time-dependent perturbation on the boundary the unlimited energy growth is observ...