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An ergodic-type theorem agravela feller for nonintegrable strictly stationary continuous time processes 

Authors: Andrew Rosalsky a;  Jordan Stoyanov b; Brett Presnell a
Affiliations:   a Department of Statistics, University of Florida, Gainesville, Florida
b Bulgarian Academy of Sciences, Institute of Mathematics, Sofia, Bulgaria
DOI: 10.1080/07362999508809417
Publication Frequency: 6 issues per year
Published in: journal Stochastic Analysis and Applications, Volume 13, Issue 5 1995 , pages 555 - 572
Formats available: PDF (English)
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Abstract

For a measurable strictly stationary continuous time stochastic process./LSAA_A_8809417_O_XML_IMAGES/LSAA_A_8809417_O_ILM0001.gif  , an analogue of a classical generalized strong law of large numbers of Feller is obtained. Specifically, it is shown that if ./LSAA_A_8809417_O_XML_IMAGES/LSAA_A_8809417_O_ILM0002.gif  where b-1is the inverse of the positive continuous function

btsatisfying ./LSAA_A_8809417_O_XML_IMAGES/LSAA_A_8809417_O_ILM0003.gif  almost certainly.Illustrative examples are provided and some open questions are outlined
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