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A limit theorem related to a new class of self similar processes. (English) Zbl 0396.60037

60G10 Stationary stochastic processes
60E07 Infinitely divisible distributions; stable distributions
60F05 Central limit and other weak theorems
Full Text: DOI
[1] Billingsley, P.: Convergence of probability measures. New York: Wiley 1968 · Zbl 0172.21201
[2] Boylan, E.: Local times for a class of Markoff processes. Illinois J. Math. 8, 19-39 (1964) · Zbl 0126.33702
[3] Darling, D.A., Kac, M.: On occupation times for Markoff processes. Trans. Amer. Math. Soc. 84, 444-458 (1957) · Zbl 0078.32005 · doi:10.1090/S0002-9947-1957-0084222-7
[4] Dobrushin, R.L.: Gaussian and their subordinated self-similar random generalized fields. Ann. Probability 7, 1-28 (1979) · Zbl 0392.60039 · doi:10.1214/aop/1176995145
[5] Dobrushin, R.L., Major, P.: Non central limit theorems for non linear functionals of Gaussian fields. [Z. Wahrscheinlichkeitstheorie verw. Gebiete, to appear · Zbl 0397.60034
[6] Feller, W.: An introduction to probability theory and its applications. Vol. II, 2nd ed. N.Y.: Wiley 1971 · Zbl 0219.60003
[7] Getoor, R.K., Kesten, H.: Continuity of local times for Markov processes. Compositio Math. 24, 277-303 (1972) · Zbl 0293.60069
[8] Gikhman, I.I., Skorokhod, A.V.: Introduction to the theory of random processes. Philadelphia: Saunders 1969 · Zbl 0132.37902
[9] Gnedenko, B.V., Kolmogorov, A.N.: Limit distributions for sums of independent random variables. Reading: Addison-Wesley 1954 · Zbl 0056.36001
[10] Ito, K.: Stochastic processes. Aarhus University Lecture Notes Series, No. 16, 1969
[11] Kesten, H., Kozlov, M.V., Spitzer, F.: A limit law for random walk in a random environment. Compositio Math. 30, 145-168 (1975) · Zbl 0388.60069
[12] Lamperti, J.: Semi-stable stochastic processes. Trans. Amer. Math. Soc. 104, 62-78 (1962) · Zbl 0286.60017 · doi:10.1090/S0002-9947-1962-0138128-7
[13] Meyer, P.A.: Un cours sur les integrales stochastiques, Séminaire de Probabilités X. Univ. de Strasbourg. Lecture Notes in Math. 511. Berlin-Heidelberg-New York: Springer 1976
[14] Spitzer, F.L.: Principles of random walk. 2nd ed. N.Y.: Springer 1976 · Zbl 0359.60003
[15] Stone, C.J.: On local and ratio limit theorems. Proc. 5-th Berkeley Sympos. Math. Statist. Probab. Univ. Calif. 217-224, 1966
[16] Taqqu, M.: Convergence of integrated processes of arbitrary Hermite rank. [To appear in Z. Wahrscheinlichkeitstheorie verw. Gebiete] · Zbl 0397.60028
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