Drift and Regularity
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Using the finiteness of the invariant measure to classify two different levels of stability is intuitively appealing. It is simple, and it also involves a fundamental stability requirement of many classes of models. Indeed, in time series analysis for example, a standard starting point, rather than an end-point, is the requirement that the model be stationary, and it follows from (10.4) that for a stationary version of a model to exist we are in effect requiring that the structure of the model be positive recurrent.
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