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Volumn 31, Issue 2, 2003, Pages 1097-1141

Measuring the range of an additive Lévy process

Author keywords

Additive L vy processes; Capacity; Energy; Hausdorff dimension; Local times; Strictly stable processes

Indexed keywords


EID: 0038674531     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1048516547     Document Type: Article
Times cited : (39)

References (36)
  • 2
    • 0038771515 scopus 로고
    • Sur la règularitè des trajectoires des martingales deux indices
    • BAKRY, D. (1979). Sur la règularitè des trajectoires des martingales deux indices. Z. Wahrsch. Verw. Gebiete 50 149-157.
    • (1979) Z. Wahrsch. Verw. Gebiete , vol.50 , pp. 149-157
    • Bakry, D.1
  • 3
    • 0038433626 scopus 로고
    • Asymptotic formulas for symmetric stable semigroups
    • BENDIKOV, A. (1994). Asymptotic formulas for symmetric stable semigroups. Expo. Math. 12 381-384.
    • (1994) Expo. Math. , vol.12 , pp. 381-384
    • Bendikov, A.1
  • 5
    • 0000361942 scopus 로고
    • Sample functions of stochastic processes with stationary independent increments
    • BLUMENTHAL, R. M. and GETOOR, R. (1961). Sample functions of stochastic processes with stationary independent increments. J. Math. Mech. 10 493-516.
    • (1961) J. Math. Mech. , vol.10 , pp. 493-516
    • Blumenthal, R.M.1    Getoor, R.2
  • 6
    • 0010660710 scopus 로고
    • Résultats de Kesten sur les processus à accroisements indépendants
    • Séminaire de Probabilités V. Springer, Berlin
    • BRETAGNOLLE, J. (1971). Résultats de Kesten sur les processus à accroisements indépendants. Séminaire de Probabilités V. Lecture Notes in Math. 191 21-36. Springer, Berlin.
    • (1971) Lecture Notes in Math. , vol.191 , pp. 21-36
    • Bretagnolle, J.1
  • 7
    • 0002029239 scopus 로고
    • Une inégalité pour martingales à indices multiples et ses applications
    • Séminaire de Probabilités VI. Springer, Berlin
    • CAIROLI, R. (1970). Une inégalité pour martingales à indices multiples et ses applications. Séminaire de Probabilités VI. Lecture Notes in Math. 124 1-27. Springer, Berlin.
    • (1970) Lecture Notes in Math. , vol.124 , pp. 1-27
    • Cairoli, R.1
  • 10
    • 0001287276 scopus 로고
    • Sample function properties of multi-parameter stable processes
    • EHM, W. (1981). Sample function properties of multi-parameter stable processes. Z. Wahrsch. Verw. Gebiete 56 195-228.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 195-228
    • Ehm, W.1
  • 11
    • 0005439109 scopus 로고
    • Multiple points in the sample paths of a Lévy process
    • EVANS, S. N. (1987a). Multiple points in the sample paths of a Lévy process. Probab. Theory Related Fields 76 359-367.
    • (1987) Probab. Theory Related Fields , vol.76 , pp. 359-367
    • Evans, S.N.1
  • 12
    • 0005409298 scopus 로고
    • Potential theory for a family of several Markov processes
    • EVANS, S. N. (1987b). Potential theory for a family of several Markov processes. Ann. Inst. H. Poincaré Probab. Statist. 23 499-530.
    • (1987) Ann. Inst. H. Poincaré Probab. Statist. , vol.23 , pp. 499-530
    • Evans, S.N.1
  • 14
    • 0000312121 scopus 로고
    • Sample functions of stochastic processes with stationary, independent increments
    • FRISTEDT, B. (1974). Sample functions of stochastic processes with stationary, independent increments. Advances in Probability and Related Topics 3 241-396.
    • (1974) Advances in Probability and Related Topics , vol.3 , pp. 241-396
    • Fristedt, B.1
  • 15
    • 0002902384 scopus 로고
    • Occupation densities
    • GEMAN, D. and HOROWITZ, J. (1980). Occupation densities. Ann. Probab. 8 1-67.
    • (1980) Ann. Probab. , vol.8 , pp. 1-67
    • Geman, D.1    Horowitz, J.2
  • 16
    • 0001928818 scopus 로고
    • A lower Lipschitz condition for the stable subordinator
    • HAWKES, J. (1971). A lower Lipschitz condition for the stable subordinator. Z. Wahrsch. Verw. Gebiete 17 23-32.
    • (1971) Z. Wahrsch. Verw. Gebiete , vol.17 , pp. 23-32
    • Hawkes, J.1
  • 17
    • 0038094780 scopus 로고
    • Local times and zero sets for processes with infinitely divisible distributions
    • HAWKES, J. (1974) Local times and zero sets for processes with infinitely divisible distributions. J. London Math. Soc. 8 517-525.
    • (1974) J. London Math. Soc. , vol.8 , pp. 517-525
    • Hawkes, J.1
  • 18
    • 0001192121 scopus 로고
    • Potential theory of Lévy processes
    • HAWKES, J. (1979). Potential theory of Lévy processes. Proc. London Math. Soc. 38 335-352.
    • (1979) Proc. London Math. Soc. , vol.38 , pp. 335-352
    • Hawkes, J.1
  • 19
    • 29144503868 scopus 로고
    • Local times as stationary processes
    • K. D. Ellworthy, ed. Longman, Chicago
    • HAWKES, J. (1986). Local times as stationary processes. In From Local Times to Global Geometry (K. D. Ellworthy, ed.) 111-120. Longman, Chicago.
    • (1986) From Local Times to Global Geometry , pp. 111-120
    • Hawkes, J.1
  • 20
    • 0038094796 scopus 로고
    • A uniform lower bound for Hausdorff dimension for transient symmetric Lévy processes
    • HENDRICS, W. J. (1983). A uniform lower bound for Hausdorff dimension for transient symmetric Lévy processes. Ann. Probab. 11 589-592.
    • (1983) Ann. Probab. , vol.11 , pp. 589-592
    • Hendrics, W.J.1
  • 21
    • 0001278145 scopus 로고
    • Potential theory related to some multiparameter processes
    • HIRSCH, F. (1995). Potential theory related to some multiparameter processes. Potential Anal. 4 245-267.
    • (1995) Potential Anal. , vol.4 , pp. 245-267
    • Hirsch, F.1
  • 22
    • 21844493266 scopus 로고
    • Symmetric Skorohod topology on n-variable functions and hierarchical Markov properties of n-parameter processes
    • HIRSCH, F. and SONG, S. (1995a). Symmetric Skorohod topology on n-variable functions and hierarchical Markov properties of n-parameter processes. Probab. Theory Related Fields 103 25-43.
    • (1995) Probab. Theory Related Fields , vol.103 , pp. 25-43
    • Hirsch, F.1    Song, S.2
  • 23
    • 21844515076 scopus 로고
    • Markov properties of multiparameter processes and capacities
    • HIRSCH, F. and SONG, S. (1995b). Markov properties of multiparameter processes and capacities. Probab. Theory Related Fields 103 45-71.
    • (1995) Probab. Theory Related Fields , vol.103 , pp. 45-71
    • Hirsch, F.1    Song, S.2
  • 24
    • 21844494244 scopus 로고
    • Some fractal sets determined by stable processes
    • HU, X. (1994). Some fractal sets determined by stable processes. Probab. Theory Related Fields 100 205-225.
    • (1994) Probab. Theory Related Fields , vol.100 , pp. 205-225
    • Hu, X.1
  • 27
    • 0013249791 scopus 로고    scopus 로고
    • Level sets of additive random walks
    • E. Giné, D. M. Mason and J. A. Wellner, eds. Birkhäuser, Basel
    • KHOSHNEVISAN, D. and XIAO, Y. (2000). Level sets of additive random walks. In High Dimensional Probability (E. Giné, D. M. Mason and J. A. Wellner, eds.) 329-345. Birkhäuser, Basel.
    • (2000) High Dimensional Probability , pp. 329-345
    • Khoshnevisan, D.1    Xiao, Y.2
  • 28
    • 0035993022 scopus 로고    scopus 로고
    • Level sets of additive Lévy processes
    • KHOSHNEVISAN, D. and XIAO, Y. (2002a). Level sets of additive Lévy processes. Ann. Probab. 30 62-100.
    • (2002) Ann. Probab. , vol.30 , pp. 62-100
    • Khoshnevisan, D.1    Xiao, Y.2
  • 29
    • 0038771507 scopus 로고    scopus 로고
    • Weak unimodality of finite measures, and an application to potential theory of additive Lévy processes
    • To appear
    • KHOSHNEVISAN, D. and XIAO, Y. (2002b). Weak unimodality of finite measures, and an application to potential theory of additive Lévy processes. Proc. Amer. Math. Soc. To appear.
    • (2002) Proc. Amer. Math. Soc.
    • Khoshnevisan, D.1    Xiao, Y.2
  • 31
    • 0038433609 scopus 로고
    • Polar sets for processes with stationary independent increments
    • J. Chover, ed. Wiley, New York
    • OREY, S. (1967). Polar sets for processes with stationary independent increments. In Markov Processes and Potential Theory (J. Chover, ed.) 117-126. Wiley, New York.
    • (1967) Markov Processes and Potential Theory , pp. 117-126
    • Orey, S.1
  • 32
    • 0038433591 scopus 로고
    • The Hausdorff dimension of the range of a process with stationary independent increments
    • PRUITT, W. E. (1969). The Hausdorff dimension of the range of a process with stationary independent increments. J. Math. Mech. 19 371-378.
    • (1969) J. Math. Mech. , vol.19 , pp. 371-378
    • Pruitt, W.E.1
  • 33
    • 0030519891 scopus 로고    scopus 로고
    • Packing and covering indices for a general Lévy process
    • PRUITT, W. E. and TAYLOR, S. J. (1996). Packing and covering indices for a general Lévy process. Ann. Probab. 24 971-986.
    • (1996) Ann. Probab. , vol.24 , pp. 971-986
    • Pruitt, W.E.1    Taylor, S.J.2
  • 35
    • 0038433594 scopus 로고
    • Sample path properties of processes with stationary independent increments
    • Wiley, London
    • TAYLOR, S. J. (1973). Sample path properties of processes with stationary independent increments. In Stochastic Analysis (A Tribute to the Memory of Rollo Davidson) 387-414. Wiley, London.
    • (1973) Stochastic Analysis (A Tribute to the Memory of Rollo Davidson) , pp. 387-414
    • Taylor, S.J.1
  • 36
    • 0001164931 scopus 로고
    • Martingales with a multidimensional parameter and stochastic integrals in the plane
    • Springer, Berlin
    • WALSH, J. B. (1986). Martingales with a multidimensional parameter and stochastic integrals in the plane. Lecture Notes in Math. 1215 329-491. Springer, Berlin.
    • (1986) Lecture Notes in Math. , vol.1215 , pp. 329-491
    • Walsh, J.B.1


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