메뉴 건너뛰기




Volumn 12, Issue 2, 1999, Pages 313-346

Hausdorff and Packing Measures of the Level Sets of Iterated Brownian Motion

Author keywords

Hausdorff measure; Iterated Brownian motion; Level set; Local time; Packing measure

Indexed keywords


EID: 0042638003     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1021669809625     Document Type: Article
Times cited : (8)

References (39)
  • 1
    • 0000670023 scopus 로고
    • On the law of the iterated logarithm for Gaussian processes
    • Arcones, M. A. (1995). On the law of the iterated logarithm for Gaussian processes. J. Theoret. Prob. 8, 877-903.
    • (1995) J. Theoret. Prob. , vol.8 , pp. 877-903
    • Arcones, M.A.1
  • 2
    • 0039710545 scopus 로고
    • Two uniform intrinsic constructions for the local time of a class of Lévy processes
    • Barlow, M. T., Perkins, E. A., and Taylor, S. J. (1986). Two uniform intrinsic constructions for the local time of a class of Lévy processes. Illinois J. Math. 30, 19-65.
    • (1986) Illinois J. Math. , vol.30 , pp. 19-65
    • Barlow, M.T.1    Perkins, E.A.2    Taylor, S.J.3
  • 4
    • 0030119978 scopus 로고    scopus 로고
    • Iterated Brownian motion and stable (1/4) subordinator
    • Bertoin, J. (1996). Iterated Brownian motion and stable (1/4) subordinator. Statist. Prob. Letters 27, 111-114.
    • (1996) Statist. Prob. Letters , vol.27 , pp. 111-114
    • Bertoin, J.1
  • 5
    • 0009391405 scopus 로고    scopus 로고
    • Hirsch's integral test for the iterated Brownian motion
    • J. Azéma, M. Émery, and M. Yor (eds.), Springer, Berlin
    • Bertoin, J., and Shi, Z. (1996). Hirsch's integral test for the iterated Brownian motion. In J. Azéma, M. Émery, and M. Yor (eds.), Sém. Probab. XXX, Lect. Notes in Math., Springer, Berlin, 1626, 361-368.
    • (1996) Sém. Probab. XXX, Lect. Notes in Math. , vol.1626 , pp. 361-368
    • Bertoin, J.1    Shi, Z.2
  • 6
    • 0000268170 scopus 로고
    • Sur la loi des temps locaux Browniens pris en un temps exponentiel
    • Springer, Berlin
    • Biane, Ph., and Yor, M. (1988). Sur la loi des temps locaux Browniens pris en un temps exponentiel. Sém. Probab. XXII, Lect. Notes in Math., Springer, Berlin, 1321, 454-466.
    • (1988) Sém. Probab. XXII, Lect. Notes in Math. , vol.1321 , pp. 454-466
    • Biane, Ph.1    Yor, M.2
  • 7
    • 0002163527 scopus 로고
    • Some path properties of iterated Brownian motion
    • E. Çinlar, K. L. Chung, M. and Sharpe (eds.), Birkhäuser, Boston
    • Burdzy, K. (1993). Some path properties of iterated Brownian motion. In E. Çinlar, K. L. Chung, M. and Sharpe (eds.), Seminar on Stochastic Processes, Birkhäuser, Boston, pp. 67-87.
    • (1993) Seminar on Stochastic Processes , pp. 67-87
    • Burdzy, K.1
  • 9
    • 0000091243 scopus 로고
    • The levels sets of iterated Brownian motion
    • J. Azéma, M. Émery, P. A. Meyer, and M. Yor (eds.), Springer, Berlin
    • Burdzy, K., and Khoshnevisan, D. (1995). The levels sets of iterated Brownian motion. In J. Azéma, M. Émery, P. A. Meyer, and M. Yor (eds.), Sém. Probab. XXIX, Lect. Notes in Math., Springer, Berlin, 1613, 231-236.
    • (1995) Sém. Probab. XXIX, Lect. Notes in Math. , vol.1613 , pp. 231-236
    • Burdzy, K.1    Khoshnevisan, D.2
  • 10
    • 0032222165 scopus 로고    scopus 로고
    • Brownian motion in a Brownian crack
    • Burdzy, K., and Khoshnevisan, D. (1998). Brownian motion in a Brownian crack. Ann. Appl. Prob. 8, 708-748.
    • (1998) Ann. Appl. Prob. , vol.8 , pp. 708-748
    • Burdzy, K.1    Khoshnevisan, D.2
  • 11
    • 84968502795 scopus 로고
    • On the maximum partial sums of sequences of independent random variables
    • Chung, K. L. (1948). On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. 64, 205-233.
    • (1948) Trans. Amer. Math. Soc. , vol.64 , pp. 205-233
    • Chung, K.L.1
  • 12
    • 0001676340 scopus 로고
    • Global Strassen type theorems for iterated Brownian motion
    • Csáki, E., Csörgo, M., Földes, A., and Révész, P. (1995). Global Strassen type theorems for iterated Brownian motion. Stoch. Proc. Appl. 59, 321-341.
    • (1995) Stoch. Proc. Appl. , vol.59 , pp. 321-341
    • Csáki, E.1    Csörgo, M.2    Földes, A.3    Révész, P.4
  • 14
    • 0031572646 scopus 로고    scopus 로고
    • On the occupation time of an iterated process having no local time
    • Csáki, E., Csörgo, M., Földes, A., and Révész, P. (1997). On the occupation time of an iterated process having no local time. Stoch. Proc. Appl. 70, 199-217.
    • (1997) Stoch. Proc. Appl. , vol.70 , pp. 199-217
    • Csáki, E.1    Csörgo, M.2    Földes, A.3    Révész, P.4
  • 15
    • 21744446851 scopus 로고    scopus 로고
    • Strassen-type theorems for a class of iterated processes
    • Csáki, E., Földes, A., and Révész, P. (1997). Strassen-type theorems for a class of iterated processes. Trans. Amer. Math. Soc. 349, 1153-1167.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 1153-1167
    • Csáki, E.1    Földes, A.2    Révész, P.3
  • 18
    • 0040553077 scopus 로고
    • The packing measure of a general subordinator
    • Fristedt, B. E., and Taylor, S. J. (1992). The packing measure of a general subordinator. Prob. Theor. Rel. Fields 92, 493-510.
    • (1992) Prob. Theor. Rel. Fields , vol.92 , pp. 493-510
    • Fristedt, B.E.1    Taylor, S.J.2
  • 19
    • 0001601561 scopus 로고
    • A probabilistic construction of the solution of some higher order parabolic differential equations
    • Funaki, T. (1979). A probabilistic construction of the solution of some higher order parabolic differential equations. Proc. Japan Acad. 55, 176-179.
    • (1979) Proc. Japan Acad. , vol.55 , pp. 176-179
    • Funaki, T.1
  • 20
    • 0000246731 scopus 로고
    • Laws of the iterated logarithm for iterated Wiener processes
    • Hu, Y., Pierre-Loti-Viaud, D., and Shi, Z. (1995). Laws of the iterated logarithm for iterated Wiener processes. J. Theor. Prob. 8, 303-319.
    • (1995) J. Theor. Prob. , vol.8 , pp. 303-319
    • Hu, Y.1    Pierre-Loti-Viaud, D.2    Shi, Z.3
  • 21
    • 0000613453 scopus 로고
    • The Csörgo-Révész modulus of non-differentiability of iterated Brownian motion
    • Hu, Y., and Shi, Z. (1995). The Csörgo-Révész modulus of non-differentiability of iterated Brownian motion. Stoch. Proc. Appl. 58, 267-279.
    • (1995) Stoch. Proc. Appl. , vol.58 , pp. 267-279
    • Hu, Y.1    Shi, Z.2
  • 22
    • 21344452030 scopus 로고    scopus 로고
    • Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations
    • Hochberg, K. J., and Orsingher, E. (1996). Composition of stochastic processes governed by higher-order parabolic and hyperbolic equations. J. Theor. Probab. 9, 511-532.
    • (1996) J. Theor. Probab. , vol.9 , pp. 511-532
    • Hochberg, K.J.1    Orsingher, E.2
  • 23
    • 0347061075 scopus 로고    scopus 로고
    • Chung's law of the iterated logarithm for the iterated Brownian motion
    • Khoshnevisan, D., and Lewis, T. M. (1996). Chung's law of the iterated logarithm for the iterated Brownian motion. Ann. Inst. Henri Poincaré 32, 349-359.
    • (1996) Ann. Inst. Henri Poincaré , vol.32 , pp. 349-359
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 24
    • 21344473661 scopus 로고    scopus 로고
    • The modulus of continuity for iterated Brownian motion
    • Khoshnevisan, D., and Lewis, T. M. (1996). The modulus of continuity for iterated Brownian motion. J. Theor. Prob. 9, 317-333.
    • (1996) J. Theor. Prob. , vol.9 , pp. 317-333
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 25
    • 0033249371 scopus 로고    scopus 로고
    • Stochastic calculus for Brownian motion on a Brownian fracture
    • to appear
    • Khoshnevisan, D., and Lewis, T. M. (1999). Stochastic calculus for Brownian motion on a Brownian fracture. Ann. Appl. Prob. (to appear).
    • (1999) Ann. Appl. Prob.
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 26
    • 84972502566 scopus 로고
    • A note on the Borel-Cantelli lemma
    • Kochen, S. B., and Stone, C. J. (1964). A note on the Borel-Cantelli lemma. Illinois J. Math. 8, 248-251.
    • (1964) Illinois J. Math. , vol.8 , pp. 248-251
    • Kochen, S.B.1    Stone, C.J.2
  • 27
    • 0005410024 scopus 로고
    • The exact Hausdorff measure of the level sets of Brownian motion
    • Perkins, E. (1980). The exact Hausdorff measure of the level sets of Brownian motion. Z. Wahrsch. verw Geb. 58, 373-388.
    • (1980) Z. Wahrsch. Verw Geb. , vol.58 , pp. 373-388
    • Perkins, E.1
  • 28
    • 84966248148 scopus 로고
    • On the iterated logarithm law for local time
    • Perkins, E. (1981). On the iterated logarithm law for local time. Proc. Amer. Math. Soc. 81, 470-472.
    • (1981) Proc. Amer. Math. Soc. , vol.81 , pp. 470-472
    • Perkins, E.1
  • 29
    • 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. Prob. 24, 971-986.
    • (1996) Ann. Prob. , vol.24 , pp. 971-986
    • Pruitt, W.E.1    Taylor, S.J.2
  • 31
    • 0000975672 scopus 로고
    • Lower limits of iterated Wiener processes
    • Shi, Z. (1995). Lower limits of iterated Wiener processes. Statist. Prob. Lett. 23, 259-270.
    • (1995) Statist. Prob. Lett. , vol.23 , pp. 259-270
    • Shi, Z.1
  • 32
    • 0037509571 scopus 로고    scopus 로고
    • Integrability and lower limits of the local time of iterated Brownian motion
    • Shi, Z., and Yor, M. (1997). Integrability and lower limits of the local time of iterated Brownian motion. Studia Scientiarum Math. Hung. 33, 279-298.
    • (1997) Studia Scientiarum Math. Hung. , vol.33 , pp. 279-298
    • Shi, Z.1    Yor, M.2
  • 33
    • 84972567300 scopus 로고
    • Sample path properties of ergodic self-similar processes
    • Takashima, K. (1989). Sample path properties of ergodic self-similar processes. Osaka J. Math. 26, 159-189.
    • (1989) Osaka J. Math. , vol.26 , pp. 159-189
    • Takashima, K.1
  • 34
    • 84974022175 scopus 로고
    • The measure theory of random fractals
    • Taylor, S. J. (1986). The measure theory of random fractals. Math. Proc. Camb. Phi. Soc. 100, 383-425.
    • (1986) Math. Proc. Camb. Phi. Soc. , vol.100 , pp. 383-425
    • Taylor, S.J.1
  • 35
    • 0043285917 scopus 로고
    • The use of packing measure in the analysis of random sets
    • Proc. 15th Symp. Stoch. Proc. Appl., Springer, Berlin
    • Taylor, S. J. (1987). The use of packing measure in the analysis of random sets. Proc. 15th Symp. Stoch. Proc. Appl., Springer, Berlin, Lect. Notes Math. 1203, 214-222.
    • (1987) Lect. Notes Math. , vol.1203 , pp. 214-222
    • Taylor, S.J.1
  • 36
    • 84966224394 scopus 로고
    • Packing measure and its evaluation for a Brownian path
    • Taylor, S. J., and Tricot, C. (1985). Packing measure and its evaluation for a Brownian path. Trans. Amer. Math. Soc. 288, 679-699.
    • (1985) Trans. Amer. Math. Soc. , vol.288 , pp. 679-699
    • Taylor, S.J.1    Tricot, C.2
  • 37
    • 0001554167 scopus 로고
    • The exact Hausdorff measure of the zero set of a stable process
    • Taylor, S. J., and Wendel, J. G. (1966). The exact Hausdorff measure of the zero set of a stable process. Z. Wahrsch. verw Geb. 6, 170-180.
    • (1966) Z. Wahrsch. Verw Geb. , vol.6 , pp. 170-180
    • Taylor, S.J.1    Wendel, J.G.2
  • 38
    • 0031231764 scopus 로고    scopus 로고
    • Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields
    • Xiao, Y. (1997). Hölder conditions for the local times and the Hausdorff measure of the level sets of Gaussian random fields. Prob. Theor. Rel. Fields 109, 129-157.
    • (1997) Prob. Theor. Rel. Fields , vol.109 , pp. 129-157
    • Xiao, Y.1
  • 39
    • 0032359434 scopus 로고    scopus 로고
    • Local times and related properties of multi-dimensional iterated Brownian motion
    • Xiao, Y. (1998). Local times and related properties of multi-dimensional iterated Brownian motion. J. Theor. Prob. 11, 383-408.
    • (1998) J. Theor. Prob. , vol.11 , pp. 383-408
    • Xiao, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.