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) no. 2, pp. 311-333. 
@article{AIHPB_1992__28_2_311_0,
     author = {Fitzsimmons, P. J. and Getoor, R. 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},
     pages = {311--333},
     publisher = {Gauthier-Villars},
     volume = {28},
     number = {2},
     year = {1992},
     mrnumber = {1162577},
     zbl = {0749.60072},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_1992__28_2_311_0/}
}
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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) no. 2, pp. 311-333. http://archive.numdam.org/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 | Zbl

[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 | Zbl

[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 | Zbl

[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 | Zbl

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

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

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

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

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

[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 | Zbl

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

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

[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 | Zbl

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

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

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

[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 | Zbl

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

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

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

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

[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 | Zbl

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

[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 | Zbl