In this article an algorithm for computing upper and lower ? approximations of a (implicitly or explicitly) given convex function h defined on an interval of length T is developed. The approximations can be obtained under weak assumptions on h (in particular, no differentiability), and the error decreases quadratically with the number of iterations. To reach an absolute accuracy of ? the number of iterations is bounded by
We present techniques for classifying Markov chains with a continuous state space as either ergodic or recurrent. These methods are analogous to those of Foster for countable space chains. The theory is presented in the first half of the paper, while the second half consists of examples illustrating these techniques. The technique for proving ergodicity involves, in practice, three steps: showing that the chain is irreducible in a suitable sense; verifying that the mean hitting times on certain (usually bounded) sets are bounded, by using a “mean drift” criterion analogous to that of Foster; and finally, checking that the chain is such that bounded mean hitting times for these sets does actually imply ergodicity. The examples comprise a number of known and new results: using our techniques we investigate random walks, queues with waiting-time-dependent service times, dams with general and random-release rules, the s-S inventory model, and feedback models. 相似文献
Advances in the study of civil war have led to the proliferation of event count data, and to a corresponding increase in the use of (zero-inflated) count models for the quantitative analysis of civil conflict events. Our ability to effectively use these techniques is met with two current limitations. First, researchers do not yet have a definitive answer as to whether zero-inflated count models are a verifiably better approach to civil conflict modeling than are ‘less assuming’ approaches such as negative binomial count models. Second, the accurate analysis of conflict-event counts with count models – zero-inflated or otherwise – is severely limited by the absence of an effective framework for the evaluation of predictive accuracy, which is an empirical approach that is of increasing importance to conflict modelers. This article rectifies both of these deficiencies. Specifically, this study presents count forecasting techniques for the evaluation and comparison of count models' predictive accuracies. Using these techniques alongside out-of-sample forecasts, it then definitively verifies – for the first time – that zero-inflated count models are superior to comparable non-inflated models for the study of intrastate conflict events. 相似文献