Limit theorems and variation properties for fractional derivatives of the local time of a stable process
Fitzsimmons, P. J. ; Getoor, R. K.
Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992), p. 311-333 / Harvested from Numdam
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@article{AIHPB_1992__28_2_311_0,
     author = {Fitzsimmons, Patrick J. and Getoor, Ronald K.},
     title = {Limit theorems and variation properties for fractional derivatives of the local time of a stable process},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {28},
     year = {1992},
     pages = {311-333},
     mrnumber = {1162577},
     zbl = {0749.60072},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_1992__28_2_311_0}
}

Fitzsimmons, P. J.; Getoor, R. K. Limit theorems and variation properties for fractional derivatives of the local time of a stable process. Annales de l'I.H.P. Probabilités et statistiques, Tome 28 (1992) pp. 311-333. http://gdmltest.u-ga.fr/item/AIHPB_1992__28_2_311_0/

[B85] M.T. Barlow, Continuity of Local Times for Lévy Processes, Z. Wahrscheinlichkeitstheorie v. Geb., Vol. 69, 1985, pp. 23-35. | MR 775850 | Zbl 0561.60076

[Ba87] R.F. Bass, Lp Inequalities for Functionals of Brownian Motion, Sém. de Probabilités, XXI; Springer Lect. Notes Math., No. 1247, 1987, pp. 206-217. | Numdam | MR 941984 | Zbl 0616.60046

[Be90] J. Bertoin, Complements on the Hilbert Transform and the Fractional Derivatives of Brownian Local Times, J. Math. Kyoto, Vol. 30, 1990, pp. 651-670. | MR 1088348 | Zbl 0725.60084

[BY87] Ph. Biane and M. Yor, Valeurs principales associées aux temps locaux browniens, Bull. Sc. Math., 2nd Ser., Vol. 111, 1987, pp. 23-101. | MR 886959 | Zbl 0619.60072

[Bi71] N.H. Bingham, Limit Theorems for Occupation Times of Markov Processes, Z. Wahrsheinlichkeitstheorie v. Geb., Vol. 17, 1971, pp. 1-22. | MR 281255 | Zbl 0194.49503

[BGT87] N.H. Bingham, C.M. Goldie and J.L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge, 1987. | MR 898871 | Zbl 0617.26001

[BG68] R.M. Blumenthal and R.K. Getoor, Markov Processes and Potential Theory, Academic Press, New York, 1968. | MR 264757 | Zbl 0169.49204

[Bo64] E.S. Boylan, Local Times for a Class of Markoff Processes, Illinois J. Math., Vol. 8, 1964, pp. 19-39. | MR 158434 | Zbl 0126.33702

[DK57] D.A. Darling and M. Kac, On Occupation Times for Markoff Processes, Trans. Am. Math. Soc., Vol. 84, 1957, pp.444-458. | MR 84222 | Zbl 0078.32005

[Da87] B. Davis, On the Barlow-Yor Inequalities for Local Time, Sém. de Probabilités, XXI; Springer Lect. Notes Math., Vol. 1247, 1987, pp. 218-220. | Numdam | MR 941985 | Zbl 0617.60041

[Du91] R. Durrett, Probability: Theory and Examples, Wadsworth and Brooks/Cole, Pacific Grove, 1991. | MR 1068527 | Zbl 0709.60002

[F80] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, Amsterdam, 1980. | MR 569058 | Zbl 0422.31007

[FG91] P.J. Fitzsimmons and R.K. Getoor, On the Distribution of the Hilbert Transform of the Local Time of a Symmetric Lévy Process, Ann. Prob. (to appear). | MR 1175273 | Zbl 0767.60071

[G90] R.K. Getoor, Excessive Measures, Birkhäuser, Boston, 1990. | MR 1093669 | Zbl 0982.31500

[GK72] R.K. Getoor and H. Kesten, Continuity of Local Times for Markov Processes, Compositio Math., Vol. 24, 1872, pp. 277-303. | Numdam | MR 310977 | Zbl 0293.60069

[HL28] G.H. Hardy and J.E. Littlewood, Some Properties of Fractional Integrals, I. Math. Zeit., Vol. 27, 1928, pp. 565-606. | JFM 54.0275.05 | MR 1544927 | Zbl 0003.15601

[K77] Y. Kasahara, Limit Theorems of Occupation Times for Markov Processes. Publ. R.I.M.S. Kyoto Univ., Vol. 12, 1977, pp. 801-818. | MR 448575 | Zbl 0367.60094

[K81] Y. Kasahara, Two Limit Theorems for Occupation Times of Markov Processes, Jpn J. Math., Vol. 7, 1981, pp. 291-300. | MR 729440 | Zbl 0483.60074

[PY86] J. Pitman and M. Yor, Asymptotic Laws of Planar Brownian Motion, Ann. Prob., Vol. 14, 1986, pp. 773-779. | MR 841582 | Zbl 0607.60070

[R75] D. Revuz, Markov Chains, North-Holland, Amsterdam, 1975. | MR 415773 | Zbl 0332.60045

[S70] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, 1970. | MR 290095 | Zbl 0207.13501

[T48] E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd ed., Clarendon Press, Oxford, 1948.

[T58] H.F. Trotter, A Property of Brownian Motion Paths, Illinois J. Math., Vol. 2, 1958, pp.425-433. | MR 96311 | Zbl 0117.35502

[Y85] T. Yamada, On the Fractional Derivative of Brownian Local Times, J. Math. Kyoto Univ., Vol. 25, 1985, pp. 49-58. | MR 777245 | Zbl 0625.60090

[Y86] T. Yamada, On Some Limit Theorems for Occupation Times of One Dimensional Brownian Motion and its Continuous Additive Functionals Locally of Zero Energy, J. Math. Kyoto Univ., Vol. 26, 1986, pp. 309-322. | MR 849222 | Zbl 0618.60080