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Volumn 9, Issue 3, 1996, Pages 717-743

The local time of iterated Brownian motion

Author keywords

Invariance principles; Iterated Brownian motion; Local time; Path properties

Indexed keywords


EID: 0043006711     PISSN: 08949840     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02214084     Document Type: Article
Times cited : (25)

References (31)
  • 1
    • 0000670023 scopus 로고
    • On the law of the iterated logarithm for Gaussian processes and their compositions
    • Arcones, M. A. (1995). On the law of the iterated logarithm for Gaussian processes and their compositions. J. Theoret. Prob. 8, 877-903.
    • (1995) J. Theoret. Prob. , vol.8 , pp. 877-903
    • Arcones, M.A.1
  • 3
    • 0009155405 scopus 로고
    • Brownian local time
    • N.S.
    • Borodin, A. N. (1989). Brownian local time (in Russian). Uspehi Mat. Nauk (N.S.) 44, (2)(266), 7-48.
    • (1989) Uspehi Mat. Nauk , vol.44 , Issue.2-266 , pp. 7-48
    • Borodin, A.N.1
  • 4
    • 27544485750 scopus 로고    scopus 로고
    • English translation
    • English translation: Russian Math. Surveys 44, 2, 1-51.
    • Russian Math. Surveys , vol.44 , Issue.2 , pp. 1-51
  • 5
    • 0002163527 scopus 로고
    • Some path properties of iterated Brownian motion
    • Çinlar, E., Chung, K. L., and Sharpe, M. (eds.), Birkhäuser, Boston
    • Burdzy, K. (1993). Some path properties of iterated Brownian motion. In Çinlar, E., Chung, K. L., and Sharpe, M. (eds.), Seminar on Stochastic Processes 1992, Birkhäuser, Boston, pp. 67-87.
    • (1993) Seminar on Stochastic Processes 1992 , pp. 67-87
    • Burdzy, K.1
  • 6
    • 0002622087 scopus 로고
    • Variation of iterated Brownian motion. Workshop and Conference on Measure-valued Processes, Stochastic Partial Differential Equations and Interacting Systems
    • Dawson, D. A. (ed.)
    • Burdzy, K. (1994). Variation of iterated Brownian motion. Workshop and Conference on Measure-valued Processes, Stochastic Partial Differential Equations and Interacting Systems. In Dawson, D. A. (ed.), CRM Proceedings and Lecture Notes 5, pp. 35-53.
    • (1994) CRM Proceedings and Lecture Notes 5 , pp. 35-53
    • Burdzy, K.1
  • 8
    • 0002580581 scopus 로고
    • How big are the increments of the local time of a Wiener process?
    • Csáki, E., Csörgo, M., Földes, A., and Révész, P. (1983). How big are the increments of the local time of a Wiener process? Ann. Prob. 11, 593-608.
    • (1983) Ann. Prob. , vol.11 , pp. 593-608
    • Csáki, E.1    Csörgo, M.2    Földes, A.3    Révész, P.4
  • 9
    • 0001694047 scopus 로고
    • Brownian local time approximated by a Wiener sheet
    • Csáki, E., Csörgo, M., Földes, A., and Révész, P. (1989). Brownian local time approximated by a Wiener sheet. Ann. Prob. 17, 516-537.
    • (1989) Ann. Prob. , vol.17 , pp. 516-537
    • Csáki, E.1    Csörgo, M.2    Földes, A.3    Révész, P.4
  • 11
    • 0001676340 scopus 로고
    • Global Strassen-type theorems for iterated Brownian motions
    • Csáki, E., Csörgo, M., Földes, A., and Révész, P. (1995). Global Strassen-type theorems for iterated Brownian motions. 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
  • 12
    • 0042907536 scopus 로고
    • How small are the increments of the local time of a Wiener process?
    • Csáki, E., and Földes, A. (1986). How small are the increments of the local time of a Wiener process? Ann. Prob. 14, 533-546.
    • (1986) Ann. Prob. , vol.14 , pp. 533-546
    • Csáki, E.1    Földes, A.2
  • 13
    • 0742318696 scopus 로고
    • A note on the stability of the local time of a Wiener process
    • Csáki, E., and Földes, A. (1987). A note on the stability of the local time of a Wiener process. Stoch. Proc. Appl. 25, 203-213.
    • (1987) Stoch. Proc. Appl. , vol.25 , pp. 203-213
    • Csáki, E.1    Földes, A.2
  • 15
    • 0002346840 scopus 로고
    • A functional LIL approach to pointwise Bahadur-Kiefer theorems
    • Dudley, R. M., Hahn, M. G., and Kuelbs, J. (eds.), Birkhäuser, Boston
    • Deheuvels, P., and Mason, D. M. (1992). A functional LIL approach to pointwise Bahadur-Kiefer theorems. In Dudley, R. M., Hahn, M. G., and Kuelbs, J. (eds.), Probability in Banach Spaces 8, Birkhäuser, Boston, pp. 255-266.
    • (1992) Probability in Banach Spaces 8 , pp. 255-266
    • Deheuvels, P.1    Mason, D.M.2
  • 16
    • 0040356922 scopus 로고
    • Two limit theorems for the simplest random walk on a line
    • N.S.
    • Dobrushin, R. L. (1955). Two limit theorems for the simplest random walk on a line (in Russian). Uspehi Mat. Nauk (N.S.) 10, (3)(65), 139-146.
    • (1955) Uspehi Mat. Nauk , vol.10 , Issue.3-65 , pp. 139-146
    • Dobrushin, R.L.1
  • 17
    • 0001601561 scopus 로고
    • Probabilistic construction of the solution of some higher order parabolic differential equations
    • Funaki, T. (1979). 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
  • 18
    • 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. Theoret. Prob. 8, 303-319.
    • (1995) J. Theoret. Prob. , vol.8 , pp. 303-319
    • Hu, Y.1    Pierre-Loti-Viaud, D.2    Shi, Z.3
  • 19
    • 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
  • 20
    • 84972521506 scopus 로고
    • An iterated logarithm law for local time
    • Kesten, H. (1965). An iterated logarithm law for local time. Duke Math. J. 32, 447-456.
    • (1965) Duke Math. J. , vol.32 , pp. 447-456
    • Kesten, H.1
  • 21
    • 85044492019 scopus 로고    scopus 로고
    • A uniform modulus result for iterated Brownian motion
    • Khoshnevisan, D., and Lewis, T. M. (1996). A uniform modulus result for iterated Brownian motion. J. Theoret. Prob.
    • (1996) J. Theoret. Prob.
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 22
    • 0347061075 scopus 로고    scopus 로고
    • Chung's law of the iterated logarithm for iterated Brownian motion
    • Khoshnevisan, D., and Lewis, T. M. (1996). Chung's law of the iterated logarithm for iterated Brownian motion. Ann. Inst. H. Poincaré.
    • (1996) Ann. Inst. H. Poincaré.
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 23
    • 0001152423 scopus 로고
    • On Bahadur's representation of sample quantiles
    • Kiefer, A. (1967). On Bahadur's representation of sample quantiles. Ann. Math. Statist. 38, 1323-1342.
    • (1967) Ann. Math. Statist. , vol.38 , pp. 1323-1342
    • Kiefer, A.1
  • 26
    • 84966248148 scopus 로고
    • On the iterated logarithm law for local time
    • Perkins, E. (1981a). 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
  • 27
    • 0005410024 scopus 로고
    • The exact Hausdorff measure of the level sets of Brownian motion
    • Perkins, E. (1981b). The exact Hausdorff measure of the level sets of Brownian motion. Z. Wahrsch. verw. Gebiete 58, 373-388.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.58 , pp. 373-388
    • Perkins, E.1
  • 28
    • 0003981318 scopus 로고
    • North Holland, Amsterdam and Akadémiai Kiadó, Budapest
    • Rényi, A. (1970). Probability Theory, North Holland, Amsterdam and Akadémiai Kiadó, Budapest.
    • (1970) Probability Theory
    • Rényi, A.1
  • 29
    • 0039930370 scopus 로고
    • Local time and invariance
    • Analytical Methods in Probability Theory, Proceedings, Oberwolfach, Germany (1980)
    • Révész, P. (1981). Local time and invariance. In: Lecture Notes in Mathematics 861, Analytical Methods in Probability Theory, Proceedings, Oberwolfach, Germany (1980), pp. 128-145.
    • (1981) Lecture Notes in Mathematics 861 , pp. 128-145
    • Révész, P.1
  • 31
    • 0000975672 scopus 로고
    • Lower limits of iterated Wiener processes
    • Shi, Z. (1995). Lower limits of iterated Wiener processes. Statist. Prob. Letters 23, 259-270.
    • (1995) Statist. Prob. Letters , vol.23 , pp. 259-270
    • Shi, Z.1


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