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Volumn 25, Issue 1, 1997, Pages 478-493

The random difference equation Xn = AnXn-1 + Bn in the critical case

Author keywords

Affine group; Limit theorem; Random coefficient autoregressive models; Random walk; Renewal theorem; Stability

Indexed keywords


EID: 0031535380     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (84)

References (30)
  • 1
    • 0040176252 scopus 로고
    • Potential at infinity on symmetric spaces and Martin boundary
    • M. Picardello, ed. Plenum Press, New York
    • BABILLOT, M. (1992). Potential at infinity on symmetric spaces and Martin Boundary. In Harmonic Analysis and Discrete Potential Theory (M. Picardello, ed.) 23-46. Plenum Press, New York.
    • (1992) Harmonic Analysis and Discrete Potential Theory , pp. 23-46
    • Babillot, M.1
  • 3
    • 0039584821 scopus 로고
    • Random affine iterated function systems: Mixing and encoding
    • M. Pinsky and V. Wihstutz, eds. Birkhäuser, Boston
    • BERGER, M. A. (1992). Random affine iterated function systems: mixing and encoding. In Diffusion Processes and Related Problems in Analysis 2 (M. Pinsky and V. Wihstutz, eds.) 315-345. Birkhäuser, Boston.
    • (1992) Diffusion Processes and Related Problems in Analysis , vol.2 , pp. 315-345
    • Berger, M.A.1
  • 5
    • 0000065881 scopus 로고
    • Exemples de théorèmes locaux sur les groupes résolubles
    • BOUGEROL, P. (1983). Exemples de théorèmes locaux sur les groupes résolubles. Ann. Inst. H. Poincaré 19 369-391.
    • (1983) Ann. Inst. H. Poincaré , vol.19 , pp. 369-391
    • Bougerol, P.1
  • 6
    • 0001523794 scopus 로고
    • Strict stationarity of generalized autoregressive processes
    • BOUGEROL, P. and PICARD, N. (1992). Strict stationarity of generalized autoregressive processes. Ann. Probab. 20 1714-1730.
    • (1992) Ann. Probab. , vol.20 , pp. 1714-1730
    • Bougerol, P.1    Picard, N.2
  • 7
    • 0039584822 scopus 로고
    • Existence of non-negative harmonic functions on groups and on covering manifolds
    • BOUGEROL, P. and ELIE, L. (1995). Existence of non-negative harmonic functions on groups and on covering manifolds. Ann. Inst. H. Poincaré 31 59-80.
    • (1995) Ann. Inst. H. Poincaré , vol.31 , pp. 59-80
    • Bougerol, P.1    Elie, L.2
  • 8
    • 0001103803 scopus 로고
    • n with stationary coefficients
    • n with stationary coefficients. Adv. in Appl. Probab. 18 211-220.
    • (1986) Adv. in Appl. Probab. , vol.18 , pp. 211-220
    • Brandt, A.1
  • 9
    • 0001676354 scopus 로고
    • Sur l'équation de convolution μ = μ * σ
    • CHOQUET, G. and DENY, J. (1960). Sur l'équation de convolution μ = μ * σ. C. R. Acad. Sci. Paris. Sér. I 250 799-801.
    • (1960) C. R. Acad. Sci. Paris. Sér. I , vol.250 , pp. 799-801
    • Choquet, G.1    Deny, J.2
  • 10
    • 0011303137 scopus 로고
    • Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point
    • COLLET, P. and FERRERO, P. (1990). Some limit ratio theorem related to a real endomorphism in case of a neutral fixed point. Ann. Inst. H. Poincaré Phys. Theor. 52 283-301.
    • (1990) Ann. Inst. H. Poincaré Phys. Theor. , vol.52 , pp. 283-301
    • Collet, P.1    Ferrero, P.2
  • 11
    • 0001661913 scopus 로고
    • Products of random matrices and computer image generation
    • DIACONIS, P. and SHAHSHAHANI, M. (1986). Products of random matrices and computer image generation. Contemp. Math. 50 173-182.
    • (1986) Contemp. Math. , vol.50 , pp. 173-182
    • Diaconis, P.1    Shahshahani, M.2
  • 12
    • 84864849879 scopus 로고
    • The distribution of a perpetuity, with applications to risk theory and pension funding
    • DUFRESNE, D. (1990). The distribution of a perpetuity, with applications to risk theory and pension funding. Scand. Actuari. J. 39-79.
    • (1990) Scand. Actuari. J. , pp. 39-79
    • Dufresne, D.1
  • 13
    • 0001414999 scopus 로고
    • Comportement asymptotique du noyau potentiel sur les groupes de Lie
    • ELIE, L. (1982). Comportement asymptotique du noyau potentiel sur les groupes de Lie. Ann. Scient. Ec. Norm. Sup. 15 257-364.
    • (1982) Ann. Scient. Ec. Norm. Sup. , vol.15 , pp. 257-364
    • Elie, L.1
  • 14
    • 0040770423 scopus 로고
    • Noyaux potentiels associés aux marches aléatoires sur les espaces homogènes. Quelques exemples clefs dont le groupe affine
    • Springer, Berlin
    • ELIE, L. (1984). Noyaux potentiels associés aux marches aléatoires sur les espaces homogènes. Quelques exemples clefs dont le groupe affine. Théorie du Potentiel. Lecture Notes in Math. 1096 223-260. Springer, Berlin.
    • (1984) Théorie du Potentiel. Lecture Notes in Math. , vol.1096 , pp. 223-260
    • Elie, L.1
  • 15
    • 84963146757 scopus 로고
    • Modelling the persistence of conditional variances
    • ENGLE, R. F. and BOLLERSLEV, T. (1986). Modelling the persistence of conditional variances. Econometric Rev. 5 1-50.
    • (1986) Econometric Rev. , vol.5 , pp. 1-50
    • Engle, R.F.1    Bollerslev, T.2
  • 16
    • 0000732230 scopus 로고
    • Implicit renewal theory and tails of solutions of random equations
    • GOLDIE, C. M. (1991). Implicit renewal theory and tails of solutions of random equations. Ann. Appl. Probab. 1 126-166.
    • (1991) Ann. Appl. Probab. , vol.1 , pp. 126-166
    • Goldie, C.M.1
  • 17
    • 0040176238 scopus 로고
    • Regular variation in the tail behavior of solutions of random difference equations
    • GREY, D. R. (1994). Regular variation in the tail behavior of solutions of random difference equations. Ann. Appl. Probab. 4 169-283.
    • (1994) Ann. Appl. Probab. , vol.4 , pp. 169-283
    • Grey, D.R.1
  • 18
    • 0010887191 scopus 로고
    • A central limit theorem for the group of linear transformations of the real axis
    • GRINCEVICIUS, A. K. (1974). A central limit theorem for the group of linear transformations of the real axis. Soviet Math. Dokl. 15 1512-1515.
    • (1974) Soviet Math. Dokl. , vol.15 , pp. 1512-1515
    • Grincevicius, A.K.1
  • 19
    • 0002158540 scopus 로고
    • A random difference equation
    • GRINCEVICIUS, A. K. (1981). A random difference equation. Lithuanian Math. J. 21 302-306.
    • (1981) Lithuanian Math. J. , vol.21 , pp. 302-306
    • Grincevicius, A.K.1
  • 20
    • 0011417751 scopus 로고
    • Théorème de classification et renouvellement pour des chaînes semi-markoviennes
    • JACOD, J. (1971). Théorème de classification et renouvellement pour des chaînes semi-markoviennes. Ann. Inst. H. Poincaré 7 83-129; (1974) 10 201-209.
    • (1971) Ann. Inst. H. Poincaré , vol.7 , pp. 83-129
    • Jacod, J.1
  • 21
    • 0040176237 scopus 로고
    • JACOD, J. (1971). Théorème de classification et renouvellement pour des chaînes semi-markoviennes. Ann. Inst. H. Poincaré 7 83-129; (1974) 10 201-209.
    • (1974) Ann. Inst. H. Poincaré , vol.10 , pp. 201-209
  • 22
    • 2942672026 scopus 로고
    • Random difference equations and renewal theory for products of random matrices
    • KESTEN, H. (1973). Random difference equations and renewal theory for products of random matrices. Acta Math. 131 207-248.
    • (1973) Acta Math. , vol.131 , pp. 207-248
    • Kesten, H.1
  • 23
    • 0001661229 scopus 로고
    • Renewal theory for functionals of Markov chain with general state space
    • KESTEN, H. (1974). Renewal theory for functionals of Markov chain with general state space. Ann. Probab. 2 355-386.
    • (1974) Ann. Probab. , vol.2 , pp. 355-386
    • Kesten, H.1
  • 24
    • 51249191002 scopus 로고
    • Conservative Markov processes on a topological space
    • LIN, M. (1970). Conservative Markov processes on a topological space. Israel J. Math. 8 165-186.
    • (1970) Israel J. Math. , vol.8 , pp. 165-186
    • Lin, M.1
  • 27
    • 0006380935 scopus 로고
    • Limit laws for a stochastic process and random recursion arising in probabilistic modeling
    • RACHEV, S. T. and SAMORODNITSKY, G. (1995). Limit laws for a stochastic process and random recursion arising in probabilistic modeling. Adv. in Appl. Probab. 27 185-202.
    • (1995) Adv. in Appl. Probab. , vol.27 , pp. 185-202
    • Rachev, S.T.1    Samorodnitsky, G.2
  • 28
    • 0003737306 scopus 로고
    • North-Holland, Amsterdam
    • REVUZ, D. (1984). Markov Chains. North-Holland, Amsterdam.
    • (1984) Markov Chains
    • Revuz, D.1
  • 29
    • 84986817203 scopus 로고
    • Some doubly stochastic time series models
    • TJØSTHEIM, D. (1986). Some doubly stochastic time series models. J. Time Series Anal. 7 51-72.
    • (1986) J. Time Series Anal. , vol.7 , pp. 51-72
    • Tjøstheim, D.1
  • 30
    • 0001565579 scopus 로고
    • On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables
    • VERVAAT, W. (1979). On a stochastic difference equation and a representation of nonnegative infinitely divisible random variables. Adv. in App. Probab. 11 750-783.
    • (1979) Adv. in App. Probab. , vol.11 , pp. 750-783
    • Vervaat, W.1


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