Propriétés de mélange des processus autorégressifs polynomiaux
Annales de l'I.H.P. Probabilités et statistiques, Tome 26 (1990) no. 2, pp. 219-260.
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     title = {Propri\'et\'es de m\'elange des processus autor\'egressifs polynomiaux},
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     url = {http://www.numdam.org/item/AIHPB_1990__26_2_219_0/}
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Mokkadem, Abdelkader. Propriétés de mélange des processus autorégressifs polynomiaux. Annales de l'I.H.P. Probabilités et statistiques, Tome 26 (1990) no. 2, pp. 219-260. http://www.numdam.org/item/AIHPB_1990__26_2_219_0/

[1] H. Akaike, Markovian Representation of Stochastic Processes, Ann. Inst. Stat. Math., vol. 26, 1974, p. 363-387. | MR | Zbl

[2] R. Azencott et D. Dacunha-CASTELLE, Séries d'observations irrégulières, Masson, Paris, 1984. | MR | Zbl

[3] J.R. Blum, D.L. Hanson et L.H. Koopmans, On the Strong Law of Large Numbers for a Class of Stochastics Processes, Z. Wahr. Verw. Gebiete, vol. 2, 1963, p. 1 - 11. | MR | Zbl

[4] Th. Bröcker, Differentiable Germs and Catastrophes, Cambridge University Press, 1975. | MR | Zbl

[5] Y.A. Davydov, Mixing Conditions for Markow Chains, Theor. Prob. Appl., vol. 28, 1973, p. 313-328. | Zbl

[6] H. Delfs et M. Knebush, Semi Algebraic Topology Over a Real Closed Fields I et II, Math. Zeit., vol. 177, 1981, p. 107-129 et vol. 178, 1981, p. 175-213. | Zbl

[7] J. Dieudonné, Éléments d'analyse, t. III, Gauthier-Villars, Paris, 1970. | MR | Zbl

[8] J.L. Doob, Stochastic Processes, Wiley, New York, 1953. | MR | Zbl

[9] V.V. Gorodetski, On the Strong Mixing Property for Linear Sequences, Theor. Prob. Appl., vol. 22, 1977, p. 411-413. | Zbl

[10] P. Hall et C.C. Heyde, Martingale Limit Theory and its Application, London Academic, 1980. | MR | Zbl

[11] R.M. Hardt, Semi Algebraic Local Triviality in Semi Algebraic Mappings, Am. J. Math., vol. 102, 1980, p. 291-302. | MR | Zbl

[12] H. Hironaka, Resolution of Singularities of an Algebraic Variety, I-II, Ann. Math., vol. 79, 1964, p. 109-326. | MR | Zbl

[13] I.A. Ibragimov et Y.V. Linnik, Independent and Stationary Sequences of Random Variables, Walth-Noordhoof Publishing Gröningen, 1974. | Zbl

[14] I.A. Ibragimov et Y. Rozanov, Processus aléatoires gaussiens, MIR, Moscou, 1974. | Zbl

[15] N. Jain et B. Jamison, Contributions to Doeblin's Theory of Markov Processes, Z. Wahr. Verw. Gebiete, vol. 8, 1967, p. 19-40. | MR | Zbl

[16] T.Y. Lam, An Introduction to Real Algebra, Rocky Mountain J. Math., vol. 14, 1984, p. 4. | MR | Zbl

[17] S. Lojasiewicz, Ensembles semi-analytiques, multigraphie de l'I.H.E.S., Bures-sur- Yvette, 1965.

[18] A. Mokkadem, Sur le mélange d'un processus ARMA vectoriel, C.R. Acad. Sci. Paris, t. 303, série I, 1986, p. 519-521. | MR | Zbl

[19] A. Mokkadem, Mixing Properties of ARMA Processes, Stoch. Proc. Appl., vol. 29, 1988, p. 309-315. | MR | Zbl

[20] A. Mokkadem, Sur un modèle autorégressif non linéaire, ergodicité et ergodicité géométrique, J.T.S.A., vol. 8, 1987, p. 195-204. | MR | Zbl

[21] A. Mokkadem, Conditions suffisantes d'existence et d'ergodicité géométrique des modè- les bilinéaires, C.R. Acad. Sci. Paris, t. 301, série I, 1985, p. 375-377. | MR | Zbl

[22] D. Mumford, Algebraic Geometry I, Complex Projective Varieties, Springer-Verlag, Berlin, 1976. | MR | Zbl

[23] J. Nash, Real Algebraic Manifolds, Ann. Math., vol. 56, 1952, p. 405-421. | MR | Zbl

[24] E. Nummelin et P. Tuominen, Geometric Ergodicity of Harris Recurrent Markov Chains, Stoch. Proc. Appl., vol. 12, 1982, p. 187-202. | MR | Zbl

[25] S. Orey, Limit Theorems for Markov Chain Transition Probabilities, Van Nostrand, London, 1971. | MR | Zbl

[26] T.D. Pham et L.T. Tran, Some Mixing Properties of Time Series Models, Stoch. Proc. Appl., vol. 19, 1986, p. 297-303. | MR | Zbl

[27] T.D. Pham, Bilinear Markovian Representation and Bilinear Models, Stoch. Proc. Appl., vol. 20, 1985, p. 295-306. | MR | Zbl

[28] M.Q. Pham, Introduction à la géométrie des variétés différentiables, Dunod, Paris, 1969. | MR | Zbl

[29] D. Revuz, Markov Chains, North Holland, Amsterdam, 1984. | MR | Zbl

[30] M. Rosenblatt, Markov Processes, Structure and Asymptotic Behaviour, Springer, Berlin, 1971. | MR | Zbl

[31] M. Rosenblatt, A Central Limit Theorem and a Strong Mixing Condition, Proc. Nat. Acad. Sci. U.S.A., vol. 42, 1956, p. 43-47. | MR | Zbl

[32] A. Seidenberg, A New Decision Method for Elementary Algebra, Ann. Math., vol. 2, 1952, p. 365-374. | MR | Zbl

[33] H. Takahata, L∞ Bounds for Asymptotic Normality of Weakly Dependent Summands Using Stein's Methods, Ann. Prob., vol. 9, 1981, p. 676-683. | MR | Zbl

[34] A.N. Tikhomirov, On the Convergence Rate in the Central Limit Theorem for Weakly Dependent Random Variables, Theor. Prob. Appl., vol. 25, 1980, p. 790-809. | MR | Zbl

[35] R.L. Tweedie, Sufficient Conditions for Ergodicity and Recurrence of Markov Chains, Stoch. Proc. Appl., vol. 3, 1975, p. 385-403. | MR | Zbl

[36] R.L. Tweedie, The Existence of Moments for Stationnary Markov Chains, J. Appl. Prob., vol. 20, 1983, p. 191-196. | MR | Zbl

[37] F.W. Warner, Foundations of Differentiable Manifolds and Lie Groups, Singer, MIT, 1971. | MR | Zbl

[38] H. Whitney, Elementary Structure of Real Algebraic Varieties, Ann. Math., vol. 66, 1957, p. 545-556. | MR | Zbl

[39] C.S. Withers, Conditions for Linear Processes to be Strong Mixing, Z. Wahr. Verw. Gebiete, vol. 57, 1981, p.481-494. | MR | Zbl

[40] R. Yokoyama, Moments Bounds for Stationnary Mixing Sequences, Z. Wahr. Verw. Gebiete, vol. 52, 1980, p.45-57. | MR | Zbl

[41] Y. Rozanov, Stationary Random Processes, Holden Day Series, 1967. | MR | Zbl

[42] E. Becker, On the Real Spectrum of a Ring and its Applications to Semi Algebraic Geometry, Bull. A.M.S., vol. 15, 1986, p. 19-60. | MR | Zbl