This note presents four sets of problems. The first suggests the possibility of a limit theory for null-recurrent renewal processes similar to the theory in the positive recurrent case. The second concerns exact coupling of random walks on the line with step-lengths that are neither discrete nor spread out. The third concerns the coupling characterization of setwise convergence of distributions...

In this paper we introduce the class of stationary prediction strategies and construct a prediction algorithm that asymptotically performs as well as the best continuous stationary strategy. We make mild compactness assumptions but no stochastic assumptions about the environment. In particular, no assumption of stationarity is made about the environment, and the stationarity of the considered s...

We connect known results about diffusion limits of Markov chain Monte Carlo (MCMC) algorithms to the Computer Science notion of algorithm complexity. Our main result states that any diffusion limit of a Markov process implies a corresponding complexity bound (in an appropriate metric). We then combine this result with previously-known MCMC diffusion limit results to prove that under appropriate...

In this paper we study the wide sense stationarity of the energy of the underwater acoustic channel impulse response and we provide an estimate of the interval during which the wide sense stationarity property holds. We analyze the SPACE08 data set, which has been collected near Martha’s Vineyard Island during October 2008. In this data set the environmental conditions such as the height of the...

The use of Artificial Neural Networks (ANN) has received increasing attention in the analysis and prediction of financial time series. Stationarity of the observed financial time series is the basic underlying assumption in the practical application of ANN on financial time series. In this paper, we will investigate whether it is feasible to relax the stationarity condition to non-stationary ti...

We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a trad...

It is demonstrated how to represent asymptotically mean stationary (AMS) random sources with values in standard spaces as mixtures of ergodic AMS sources. This an extension of the well known decomposition of stationary sources which has facilitated the generalization of prominent source coding theorems to arbitrary, not necessarily ergodic, stationary sources. Asymptotic mean stationarity gener...

We consider optimization problems in Banach spaces involving a complementarity constraint defined by a convex cone K. By transferring the local decomposition approach, we define strong stationarity conditions and provide a constraint qualification under which these conditions are necessary for optimality. To apply this technique, we provide a new uniqueness result for Lagrange multipliers in Ba...

In spite of the undisputedly high degree of non-stationarity of speech signals, the present day determination of its acoustic features is based on the assumption that speech production can be described as a linear time invariant (LTI) system on the time scale of about 20 ms [1]. In automatic speech recognition, the wide sense stationarity of an LTI–system is used as prerequisite for the consist...

We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J -function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to th...