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The Annals of Probability
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The Annals of Probability
Article . 1988 . Peer-reviewed
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Backward Limits

Backward limits
Authors: Thorisson, Hermann;

Backward Limits

Abstract

The author raised the question: Start the process at an arbitrary time s and check what happens to its distribution in a fixed time interval [t,\(\infty)\) as the starting time s goes backward to -\(\infty\). Backward limits are considered for time-inhomogeneous regenerative processes introduced by the author [Adv. Appl. Probab. 15, 531-561 (1983; Zbl 0512.60080)]. The existence of a two-sided time-inhomogeneous limit (in the sense of total variation) process, which inherits the regenerative properties, is proved, under regularity conditions on the regeneration times.

Keywords

Markov processes, inhomogeneous regeneration, inhomogeneous Markov process, General theory of stochastic processes, regeneration times, Generalized stochastic processes, regenerative process, 60G07, existence of a two-sided time-inhomogeneous limit, two-sided process, 60J99, Backward limits, 60G20, regenerative properties

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
7
Average
Top 10%
Average
Green
hybrid