메뉴 건너뛰기




Volumn 11, Issue , 2006, Pages 434-459

Laws of the iterated logarithm for α-time brownian motion

Author keywords

Brownian motion; Chung s law; Kesten s law; Local time; Symmetric stable process; time Brownian motion

Indexed keywords


EID: 33745321212     PISSN: None     EISSN: 10836489     Source Type: Journal    
DOI: 10.1214/EJP.v11-327     Document Type: Article
Times cited : (10)

References (29)
  • 1
    • 0035470879 scopus 로고    scopus 로고
    • Brownian-time processes: The pde connection and the halfderivative generator
    • H. Allouba and W. Zheng, Brownian-time processes: The pde connection and the halfderivative generator, Ann. Prob. 29 (2001), no. 2, 1780-1795.
    • (2001) Ann. Prob , vol.29 , Issue.2 , pp. 1780-1795
    • Allouba, H.1    Zheng, W.2
  • 2
    • 0003975247 scopus 로고    scopus 로고
    • Cambridge University Press
    • J. Bertoin, Levy processes, Cambridge University Press, (1996).
    • (1996) Levy Processes
    • Bertoin, J.1
  • 4
    • 0002163527 scopus 로고
    • Some path properties of iterated Brownian motion
    • E. Cinlar, K.L. Chung and M.J. Sharpe, eds.), Birkhauser, Boston
    • K. Burdzy, Some path properties of iterated Brownian motion, In Seminar on Stochastic Processes (E. Cinlar, K.L. Chung and M.J. Sharpe, eds.), Birkhauser, Boston, (1993), 6787.
    • (1993) Seminar on Stochastic Processes , pp. 6787
    • Burdzy, K.1
  • 7
    • 84858899204 scopus 로고    scopus 로고
    • A chung-type law of the iterated logarithm for iterated Brownian motion
    • C. C. Yin and Y. H. Lü, A chung-type law of the iterated logarithm for iterated Brownian motion, Acta. Math. Sinica 43 (2000), 99-106.
    • (2000) Acta. Math. Sinica , vol.43 , pp. 99-106
    • Yin, C.C.1    Lü, Y.H.2
  • 8
    • 84968502795 scopus 로고
    • On the maximum partial sums of sequences of independent random variables
    • K. L. Chung, On the maximum partial sums of sequences of independent random variables, Trans. Amer. Math. Soc. 64 (1948), 205-233.
    • (1948) Trans. Amer. Math. Soc , vol.64 , pp. 205-233
    • Chung, K.L.1
  • 9
    • 26844508919 scopus 로고    scopus 로고
    • Iterated Brownian motion in an open set
    • R. D. DeBlassie, Iterated Brownian motion in an open set, Ann. Appl. Prob. 14 (2004), no. 3, 1529-1558.
    • (2004) Ann. Appl. Prob , vol.14 , Issue.3 , pp. 1529-1558
    • Deblassie, R.D.1
  • 10
    • 0042907536 scopus 로고
    • How small are the increments of the local time of a Wiener process
    • E. Csaki and A. Füldes, How small are the increments of the local time of a Wiener process?, Ann. Prob. 14 (1986), 533-546.
    • (1986) Ann. Prob , vol.14 , pp. 533-546
    • Csaki, E.1    Füldes, A.2
  • 12
    • 84980138040 scopus 로고
    • On the laws of the iterated logarithm for local times
    • M.D. Donsker and S.R.S. Varadhan, On the laws of the iterated logarithm for local times, Comm. Pure Appl. Math. 30 (1977), 707-753.
    • (1977) Comm. Pure Appl. Math , vol.30 , pp. 707-753
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 13
    • 0040926002 scopus 로고
    • Laws of the iterated logarithm for symmetric stable processes
    • P.S. Griffin, Laws of the iterated logarithm for symmetric stable processes, Z. Wahrschein-lichkeitstheorie verw. Gebiete 68 (1985), 271-285.
    • (1985) Z. Wahrschein-Lichkeitstheorie Verw. Gebiete , vol.68 , pp. 271-285
    • Griffin, P.S.1
  • 14
    • 0000246731 scopus 로고
    • Laws of iterated logarithm for iterated Wiener proceses
    • Y. Hu, D. Pierre-Loti-Viaud, and Z. Shi, Laws of iterated logarithm for iterated Wiener proceses, J. Theoret. Probabl. 8 (1995), 303-319.
    • (1995) J. Theoret. Probabl , vol.8 , pp. 303-319
    • Hu, Y.1    Pierre-Lotiviaud, D.2    Shi, Z.3
  • 15
    • 0012027321 scopus 로고
    • Tauberian theorems of exponential type
    • Y. Kasahara, Tauberian theorems of exponential type, J. Math. Kyoto Univ. 12 (1978), no. 2, 209-219.
    • (1978) J. Math. Kyoto Univ , vol.12 , Issue.2 , pp. 209-219
    • Kasahara, Y.1
  • 16
    • 84972521506 scopus 로고
    • An iterated logarithm law for local time
    • H. Kesten, An iterated logarithm law for local time, Duke Math. J. 32 (1965), 447-456.
    • (1965) Duke Math. J , vol.32 , pp. 447-456
    • Kesten, H.1
  • 17
    • 0347061075 scopus 로고    scopus 로고
    • Chung’s law of the iterated logarithm for iterated Brownian motion
    • D. Khoshnevisan and T.M. Lewis, Chung’s law of the iterated logarithm for iterated Brownian motion, Ann. Inst. H. Poincare Probab. Statist. 32 (1996), no. 3, 349-359.
    • (1996) Ann. Inst. H. Poincare Probab. Statist , vol.32 , Issue.3 , pp. 349-359
    • Khoshnevisan, D.1    Lewis, T.M.2
  • 19
    • 0001482627 scopus 로고
    • Small deviations in a space of trajectories
    • A. A. Mogul’skii, Small deviations in a space of trajectories, Theor. Probab. Appl. 19 (1974), 726-736.
    • (1974) Theor. Probab. Appl , vol.19 , pp. 726-736
    • Mogul’skii, A.A.1
  • 20
    • 33645672118 scopus 로고    scopus 로고
    • Iterated Brownian motion in parabola-shaped domains
    • E. Nane, Iterated Brownian motion in parabola-shaped domains, Potential Analysis, 24 (2006), 105-123.
    • (2006) Potential Analysis , vol.24 , pp. 105-123
    • Nane, E.1
  • 21
    • 33745326651 scopus 로고    scopus 로고
    • Iterated Brownian motion in bounded domains in Rn
    • E. Nane, Iterated Brownian motion in bounded domains in Rn, Stochastic Processes and Their Applications, 116 (2006), 905-916.
    • (2006) Stochastic Processes and Their Applications , vol.116 , pp. 905-916
    • Nane, E.1
  • 24
    • 0003543379 scopus 로고
    • Continuous martingales and Brownian motion, 2nd edition
    • Springer, Berlin
    • D. Revuz and M. Yor, Continuous martingales and Brownian motion, 2nd edition, Grundlehren der mathematischen Wissenschaften, 293, Springer, Berlin, (1994).
    • (1994) Grundlehren Der Mathematischen Wissenschaften , vol.293
    • Revuz, D.1    Yor, M.2
  • 25
    • 0037509571 scopus 로고    scopus 로고
    • Integrability and lower limits of the local time of iterated Brownian motion
    • Z. Shi and M. Yor, Integrability and lower limits of the local time of iterated Brownian motion, Studia Sci. Math. Hungar. 33 (1997), no. 1-3, 279-298.
    • (1997) Studia Sci. Math. Hungar , vol.33 , Issue.1-3 , pp. 279-298
    • Shi, Z.1    Yor, M.2
  • 27
    • 0000889178 scopus 로고
    • A bibliographical guide to self-similar processes and long-range dependence
    • Dependence in Prob. And Stat. (eds.), Eberlein, M. S. Taqqu
    • M. S. Taqqu, A bibliographical guide to self-similar processes and long-range dependence, Progress in Prob. Stat. 11 (1986), 137-162. Dependence in Prob. And Stat. (eds.), Eberlein, M. S. Taqqu.
    • (1986) Progress in Prob. Stat , vol.11 , pp. 137-162
    • Taqqu, M.S.1
  • 28
    • 0001299350 scopus 로고
    • Sample path properties of a transient stable process
    • S.J. Taylor, Sample path properties of a transient stable process, J. Math. Mech. 16 (1967), 1229-1246.
    • (1967) J. Math. Mech , vol.16 , pp. 1229-1246
    • Taylor, S.J.1
  • 29
    • 0032359434 scopus 로고    scopus 로고
    • Local times and related properties of multi-dimensional iterated Brownian motion
    • Y. Xiao, Local times and related properties of multi-dimensional iterated Brownian motion, J. Theoret. Probab. 11 (1998), no. 2, 383-408.
    • (1998) J. Theoret. Probab , vol.11 , Issue.2 , pp. 383-408
    • Xiao, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.