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ON THE CONDITIONAL VERSION OF KOLMOGOROV'S THREE-SERIES THEOREM
Authors:Liu Guoxin
Affiliation:1. Key Lab of Structures Dynamic Behavior and Control of the Ministry of Education, School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China;2. Seazen Holdings Co., Ltd, 200000 Shanghai, China;1. Key Lab of Groundwater Resources and Environment, Ministry of Education, Jilin University, Changchun 130021, People’s Republic of China;2. College of New Energy and Environment, Jilin University, Changchun 130021, People’s Republic of China;3. Institute of Water Resources and Environment, Jilin University, Changchun 130021, People’s Republic of China;1. Department of Mathematics, Aarhus University, Ny Munkegade 118, DK-8000 Aarhus C, Denmark;2. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen, Denmark
Abstract:This paper studies the conditional version of Kolmogorov's three-series theorem, and gets a new extention form of the conditional version. The results here present us an answer to the question when (or where) the conditional version also provide necessary conditions for convergence in dependent cases. Furthermore, some new sufficient conditions are obtained.
Keywords:Three-series theorem   dependent r.v. 's   predictable   local absolute continuity   martingale
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