×

zbMATH — the first resource for mathematics

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

MSC:
60G10 Stationary stochastic processes
60E07 Infinitely divisible distributions; stable distributions
60F05 Central limit and other weak theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.