Limit theorems for local times of fractional Brownian motions and some other self-similar processes

Kyoto Journal of Mathematics

Volumn 36, Issue 4, 1996, Pages 641-652

  Shieh, Narn Rueih ^a  

^a NATIONAL TAIWAN UNIVERSITY   (Taiwan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030327741     PISSN: 0023608X     EISSN: None     Source Type: Journal    
DOI: 10.1215/kjm/1250518444     Document Type: Article

References (22)

1. T. Bedford and A. M. Fisher, Analogues of Lebesgue density theorem for fractal sets of real and integers, Proc. London. Math. Soc., 64(1992), 95-124.
2. S. M. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J., 23(1973), 69-94.
3. S. M. Berman, Joint continuity of local times of Markov processes, Z. Wahr. verw. Geb., 69(1985), 37-46.
4. P. Billingsley, Convergence of Probability Measures, Wiley, 1968.
5. G. A. Brosamler, The asymptotic behaviour of certain additive functionals of Brownian motion, Inventiones Math., 20(1973), 87-96.
6. I. P. Cornfeld, S.V. Fomin and Ya G. Sinai, Ergodic Theory, Springer-Verlag, 1980.
7. S. Cambanis, C. D. Hardin and A. Weson, Ergodic properties of stationary stable processes, Stochastic Processes and Appl., 24(1987), 1-18.
8. D. A. Darling and M. Kac, On occupation times for Markoff processes, Trans. Amer. Math. Soc., 84 (1957), 444-458.
9. P. J. Fitzsimmons and R. K. Getoor, Limit theorems and variation properties for fractional derivatives of the local time of a stable process, Ann. Inst. Henri Poincaré, 28(1992), 311-333.
10. D. Geman and J. Horowitz, Occupation densities, Ann. Probab., 8(1980), 1-67.
11. N. Ikeda and S. Watanabe, Stochastic differential equations and diffusion processes 2nd Edition, North-Holland & Kodansha, 1989.
12. Y. Kasahara, Limit theorems of occupation times for Markov processes, Publ. RIMS Kyoto Univ., 12(1977), 801-818.
13. N. Kôno and N. R. Shieh, Local times and related sample path properties of certain self-similar processes, J. Math. Kyoto Univ., 33(1993), 51-64.
14. N. Kôno, Kallianpur-Robbins law for fractional Brownian motion, Abstract for Japan-Russian Symposium on Probability and Math. Statistics, July 26-30, 1995.
15. M. Maejima, Self-similar processes and limit theorems, Sugaku Exposition, 2(1989), 103-123.
16. J. P. Nolan, Local nondeterminism and local times for stable processes, Probab. Th. Rel. Fields, 82(1989), 387-410.
17. J. P. Nolan, Path properties of index-β processes, Ann. Probab., 16(1988), 1596-1607.
18. L. D. Pitt, Local times for Gaussian vector fields, Indiana Univ. Math. J., 27(1978), 309-330.
19. G. Samorodnitsky and M. Taqqu, Stable non-Gaussian random processes, Chapman-Hall, 1994.
20. K. Takashima, Sample paths properties of ergodic self-similar processes, Osaka J. Math., 26 (1989), 159-189.
21. W. Vervaat, Properties of general self-similar processes, 46th session of ISI at Tokyo Japan Sept. 8-16, 1987.
22. T. Yamada, On some limit theorems for occupation times of one-dimensional Brownian motion and its continuous additive functional locally of zero energy. J. Math. Kyoto Univ., 26(1986), 309-322.