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Principle of Conditioning is a well known heuristic rule which allows constructing limit theorems for sums of dependent random variables from existing limit theorems for independent summands. In the paper we state a general limit theorem on converegnce to stable laws, which is valid for stationary sequences and provides a link between the Principle of Conditioning and ergodic theorems.
Wydawca
Czasopismo
Rocznik
Tom
Strony
325--336
Opis fizyczny
Bibliogr. 23 poz.
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autor
- Faculty Of Mathematics And Computer Science Nicolaus Copernicus University Ul.Chopina 12/18 87 100 Toruń, Poland, adjakubo@mat.umk.pl
Bibliografia
- [1] K.Bartkiewicz, A.Jakubowski, T.Mikosch, O.Wintenberger, Stable limits for sums of dependent infinite variance random variables Probab.Theory Related Fields 150 (2011),337 –372.
- [2] M.Beśka, A.Kłopotowski, L.Słomiński, Limit theorems for random sums of dependent d-dimensional random vectors Z.Wahrscheinlichkeitstheorie verw.Gebiete 61 (1982),43 –57.
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- [5] V.de la Pena, E.Giné, Decoupling: from Dependence to Independence Springer 1999.
- [6] R.Durrett, S.I.Resnick, Functional limit theorems for dependent random variables Ann.Probab.6 (1978),829 –846.
- [7] P.Embrechts, C.Klüppelberg, T.Mikosch, Modelling Extremal Events Springer 1997.
- [8] R.Engle, Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation Econometrica 50 (1982),987 –1007.
- [9] Ch.Francq, J.M.Zakoian, Garch Models. Structure, Statistical Inference and Financial Applications Wiley 2010.
- [10] J.Jacod, A.Kłopotowski, J.Me´min, Théorème de la limite centrale et convergence fonctionelle vers un processus à accroissements indépendants: la méthode des mar-tingales Ann.Inst.H.Poincaré,Sect.B 18 (1982),1 –45.
- [11] A.Jakubowski, On limit theorems for sums of dependent Hilbert space valued random variables Lecture Notes in Statist.2 (1980),178 –187.
- [12] A.Jakubowski, Principle of Conditioning Principle in limit theorems for sums of random variables Ann.Probab.14 (1986),902 –915.
- [13] A.Jakubowski, Tightness criteria for random measures with application to the Principle of Conditioning in Hilbert spaces Probab.Math.Statist.9 (1988),95 –114.
- [14] A.Jakubowski, J.Mémin, Functional central limit theorems for a class of quadratic forms in independent random variables Teor.Veroyatn.Primen.38 (1993),600 –612, (SIAM translation:Theory Probab.Appl.38 (1993),423 –432.)
- [15] M.Jara, T.Komorowski, S.Olla, Limit theorems for additive functionals of a Markov chain Ann.Appl.Probab.19 (2009),2270 –2300.
- [16] A.Kłopotowski, Limit theorems for sums of dependent random vectors in R d,Dissertationes Math.151 (1977),1 –62.
- [17] S.Kwapień and W.A.Woyczyński, Random Series and Stochastic Integrals: Single and Multiple Birkhäuser 1992.
- [18] T.Mikosch, C.Stărică, Limit theory for the sample autocorrelations and extremes of a GARCH(1, 1) process Ann.Statist.28 (2000),1427 –1451.
- [19] I.Nourdin, G.Peccati, G.Reinert, Invariance principles for homogeneous sums: universality of Gaussian Wiener Chaos Ann.Probab.38 (2010),1947 –1985.
- [20] G.Peccati, M.S.Taqqu, Stable convergence of generalized L2 stochastic integrals and the principle of conditioning Electr.J.Probab.12 (2007),447 –480.
- [21] J.Rosiński, The central limit theorems for dependent random vectors in Banach spaces Preprints of Inst.Math.of Polish Acad.Sci.241 (1981).
- [22] D.Surgailis, A quadratic ARCH(1 ) model with long memory and Lévy stable behavior of squares Adv.Appl.Probab.40 (2008),1198 –1222.
- [23] Z.Szewczak, On relative stability for strictly stationary mixing sequences to appear in Stoch.Proc.Appl.(2005+).
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Bibliografia
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bwmeta1.element.baztech-article-PWA4-0034-0030