Vector-valued Almost Sure Invariance Principle For Non-stationary Dynamical Systems

Loss of memory and moment bounds for nonstationary intermittent dynamical systems

“…As in [19], we prove concentration bounds not only for Birkhoff sums, but for a more general class of separately Lipschitz (or separately Hölder) functions on [0, 1] N , see Theorem 3.11 and Remark 3.3. Theorem 1.2 improves the moment bounds in Nicol, Pereira and Török [33] and Su [41], and implies the following bounds on large and moderate deviations: Corollary 2.1. In the notation of Theorem 1.2, for every p > 2,…”

“…Alternatively, one can use the moment bounds from [33] or [41], but these were not available when we started this project.…”

“…We study limit laws for nonstationary dynamical systems, a topic of very intense recent interest, see [2,3,4,5,9,13,14,15,16,20,22,23,29,33,34,38,40,41] and more.…”

Random Young towers and quenched limit laws

“…Using φφ • F n dμ ≤ Cn −(D−2−δ)(p−γ )/p ≤ Cn −4 and following the same computations as in the proof of Corollary 3.10 of [Su19b] (we skip this here), we have…”

Sunklodas' approach to normal approximation for time-dependent dynamical systems

“…ASIPs were obtained also by Castro et al [6] for convergent sequences of Anosov diffeomorphisms and expanding maps on compact Riemannian manifolds. Recently Su [38] proved a vector valued ASIP for a general class of polynomially mixing time-dependent systems. Among its many implications is a self-norming CLT for the sequential intermittent system with β * < 1/2, under a (polynomial) variance growth condition.…”