We introduce random towers to study almost sure rates of correlation decay for partially hyperbolic attractors. Using this framework, we obtain abstract results on exponential, stretched exponential and polynomial rates. then apply our small perturbations Axiom A attractors, derived from Anosov systems solenoidal attractors with intermittency.

a r t i c l e i n f o a b s t r a c t MSC: 34D20 34K50 60H10 93E15 Keywords: Pure delay system Two-timescale Markov chain Stationary distribution Almost sure uniform stability Yorke's condition This work examines almost sure stability of a pure random delay system whose delay time is modeled by a finite state continuous-time Markov chain with two-time scales. The Markov chain contains a fast-va...

Let a class F of densities be given. We draw an i.i.d. sample from a density f which may or may not be in F . After every n, one must make a guess whether f ∈ F or not. A class is almost surely discernible if there exists such a sequence of classification rules such that for any f , we make finitely many errors almost surely. In this paper several results are given that allow one to decide whet...

Censoring, 116 Coefficient concentration, 287 confidence, 173 uncertainty, 287 Competing risks, 371 Confidence interval, 13, 173 coverage probability, 173 unbiased, 96 uniformly most accurate, 96 Contingency tables, 274 Convergence almost certain, 120 almost sure, 120, 121 almost sure convergence of series, 164 complete, 120, 129 equivalent, 148 in distribution, 125 in law, 125 in probability, ...

This paper investigates the almost sure H∞ sliding mode control (SMC) problem for nonlinear stochastic systems with Markovian switching and time-delays. An integral sliding surface is first constructed for the addressed system. Then, by employing the stopping time method combined with martingale inequalities, sufficient conditions are established to ensure the almost surely exponential stabilit...