Abstract
In this paper, we introduce a class of nonlinear time series models with random time delay under random environment, sufficient conditions for nonergodicity of these models are developed. The so-called Markovnization methods are used, that is, proper supplementary variables are added to a non-Markov process, then a new Markov process can be obtained.
Highlights
1 Introduction By virtue of their superduper properties, stable stochastic processes are very popular among many researchers, so there has been a large literature devoted to the stable or even stationary stochastic processes
Fernandes and Grammig [ ] established conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. This owes a great deal to the beautiful properties of stable processes, such as an ergodic Markov chain has an invariant probability measure which is finite, a recurrent stochastic process re-visits an arbitrary point in its image an infinite number of times
Many researchers often like to target ergodicity or recurrence as their assumptions in their papers or books. In this colorful world, lots and lots of phenomena exhibit instability behavior, for example, David [ ] argued that an important lesson from economic history was that economies exhibited nonergodic behavior along many dimensions
Summary
By virtue of their superduper properties, stable (ergodic or recurrent) stochastic processes are very popular among many researchers, so there has been a large literature devoted to the stable (ergodic or recurrent) or even stationary stochastic processes. Fernandes and Grammig [ ] established conditions for the existence of higher-order moments, strict stationarity, geometric ergodicity and β-mixing property with exponential decay. This owes a great deal to the beautiful properties of stable processes, such as an ergodic Markov chain has an invariant probability measure which is finite, a recurrent stochastic process re-visits an arbitrary point in its image an infinite number of times. Many researchers often like to target ergodicity or recurrence as their assumptions in their papers or books. Section develops some useful lemmas and gives some sufficient conditions for nonergodicity of the proposed model as our main results.
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