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Convergence rates in the SLLN for some classes of dependent random fields |
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| Authors: | Anna Kuczmaszewska Zbigniew A Lagodowski |
| Institution: | a Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland b Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland |
| Abstract: | Let  be a random field i.e. a family of random variables indexed by Nr, r?2. We discuss complete convergence and convergence rates under assumption on dependence structure of random fields in the case of nonidentical distributions. Results are obtained for negatively associated random fields, ρ?-mixing random fields (having maximal coefficient of correlation strictly smaller then 1) and martingale random fields. |
| Keywords: | Complete convergence Negatively associated random fields _method=retrieve& _eid=1-s2 0-S0022247X11002800& _mathId=si5 gif& _pii=S0022247X11002800& _issn=0022247X& _acct=C000069490& _version=1& _userid=6211566& md5=4e860b611cbc6c838bad6eff95685055')" style="cursor:pointer ρ?-mixing random fields" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">ρ?-mixing random fields Martingale random fields Baum-Katz theorem |
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