Recently, two retractions (projections) which are different from the metric projection and the sunny nonexpansive retraction in a Banach space were found. In this paper, using nonlinear analytic methods and new retractions, we prove a nonlinear ergodic theorem for positively homogeneous and nonexpansive mappings in a uniformly convex Banach space. The limit points are characterized by using new...

We establish convergence of the nonlinear filter of the state of a randomly perturbed dynamical system in which the perturbation is a rapidly fluctuating ergodic Markov process, and the observation process conditions the state of the system. The limiting nonlinear filter is completely characterized.

In this paper we provide conditions for nonlinear time series to be geometrically explosive with positive probability. The paper complements earlier work by the authors on geometrically ergodic nonlinear time series, showing that the conditions for examples in the earlier paper are sharp. We also study the transience of polynomial autoregression models.

In a recent work [5] various Markov and ergodicity properties of the nonlinear filter, for the classical model of nonlinear filtering, were studied. It was shown that under quite general conditions, when the signal is a Feller-Markov process with values in a complete separable metric space E then the pair process (signal, filter) is also a FellerMarkov process with state space E × P(E), where P...

Abstract The Ibragimov–Khasminskii theory established a scheme that gives asymptotic properties of the likelihood estimators through convergence ratio random field. This is extending to various nonlinear stochastic processes, combined with polynomial type large deviation inequality proved for general locally asymptotically quadratic quasi-likelihood We give an overview analysis and its applicat...

* Correspondence: [email protected]. edu.tw Department of Mathematics, National Changhua University of Education, Changhua, 50058, Taiwan Full list of author information is available at the end of the article Abstract In this paper, we introduced two new classes of nonlinear mappings in Hilbert spaces. These two classes of nonlinear mappings contain some important classes of nonlinear mappings, l...

We investigate stochastic homogenization for some degenerate quasilinear parabolic PDEs. The underlying nonlinear operator degenerates along the space variable, uniformly in the nonlinear term: the degeneracy points correspond to the degeneracy points of a reference diffusion operator on the random medium. Assuming that this reference diffusion operator is ergodic, we can prove the homogenizati...

This paper presents the ergodic capacity of nonlinear MIMO-OFDM Decode-and-Forward (DF) relay network.Nonlinearities in wireless communication channels can arise at the transmitter or the receiver side. In this work, we focus on the transmitter-side nonlinearities induced by the High Power Amplifier (HPA), the last stage in the communication chain at the base station (BS) and the relay stations...

Entropy and recurrence times are two of the most important complexity measures for both random fields and nonlinear dynamical systems. We report a fundamental relation between recurrence time distribution and Renyi entropy of arbitrary integer order for both ergodic random fields and ergodic nonlinear dynamical systems, thus provide an elegant and comprehensive characterization for these two im...