Let (Xt, Yt)t∈T be a discrete or continuous-time Markov process with state space X × R where X is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. (Xt, Yt)t∈T is assumed to be a Markov additive process. In particular, this implies that the first component (Xt)t∈T is also a Markov process. Markov random walks or additive f...

For stationary ergodic diffusions satisfying nonlinear homogeneous Itô stochastic differential equations, this paper obtains the Berry–Esseen bounds on rates of convergence to normality distributions quasi maximum likelihood estimators based Taylor approximation, under some regularity conditions, when diffusion is observed at equally spaced dense time points over a long interval, high-frequency...

We establish a general Berry–Esseen type bound which gives optimal bounds in many situations under suitable moment assumptions. By combining the with Palm theory, we deduce new error for assessing accuracy of normal approximation to statistics arising from random measures, including stochastic geometry. illustrate use four examples: completely excursion measure locally dependent process, and to...

Abstract In this article, we take a probabilistic look at Hölder's inequality, considering the ratio of terms in classical Hölder inequality for random vectors . We prove central limit theorem ratio, which then allows us to reverse up multiplicative constant with high probability. The models randomness include uniform distribution on balls and spheres. also provide Berry–Esseen–type result larg...

We prove a Berry–Esseen theorem, local central limit theorem and (local) large (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain (Young) tower extensions, which main focus of this paper. On towers we will obtain our using contraction proper...