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In this paper we revisit the results of Loynes (1962) on stability of queues for ergodic arrivals and services, and show examples when the arrivals are bounded and ergodic, the service rate is constant, and under stability the limit distribution has larger than exponential tail.
The forward estimation problem for stationary and ergodic time series ${X_n}_{n=0}^{infty}$ taking values from a finite alphabet ${cal X}$ is to estimate the probability that $X_{n+1}=x$ based on the observations $X_i$, $0le ile n$ without prior know
Let ${(X_i,Y_i)}$ be a stationary ergodic time series with $(X,Y)$ values in the product space $R^dbigotimes R .$ This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance)
The setting is a stationary, ergodic time series. The challenge is to construct a sequence of functions, each based on only finite segments of the past, which together provide a strongly consistent estimator for the conditional probability of the nex
This study concerns problems of time-series forecasting under the weakest of assumptions. Related results are surveyed and are points of departure for the developments here, some of which are new and others are new derivations of previous findings. T
We present a simple randomized procedure for the prediction of a binary sequence. The algorithm uses ideas from recent developments of the theory of the prediction of individual sequences. We show that if the sequence is a realization of a stationary