메뉴 건너뛰기




Volumn 350, Issue 10, 1998, Pages 4253-4264

Chung's law for integrated brownian motion

Author keywords

Integrated brownian motion; Small ball probability

Indexed keywords


EID: 22444455671     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-98-02011-x     Document Type: Article
Times cited : (45)

References (33)
  • 1
    • 0041080553 scopus 로고    scopus 로고
    • Transience of stochastically perturbed classical Hamiltonian systems and random wave operators
    • CMP 97:09
    • Albeverio, S-, Hubert, A. and Kolokoltsov, V.N. (1997). Transience of stochastically perturbed classical Hamiltonian systems and random wave operators. Stochastics Stochastics Rep. 60. CMP 97:09
    • (1997) Stochastics Stochastics Rep. , vol.60
    • Albeverio, S.1    Hubert, A.2    Kolokoltsov, V.N.3
  • 3
    • 84968476146 scopus 로고
    • The integral of symmetric unimodular function over a symmetric convex set and some probability inequalities
    • Anderson, T.W. (1955). The integral of symmetric unimodular function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6;170-176. MR 16:1005a
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 170-176
    • Anderson, T.W.1
  • 4
    • 21144470601 scopus 로고
    • Some exact equivalents for the Brownian motion in Holder norm
    • MR 94a:60117
    • Baldi, P. and Roynette, B. (1992). Some exact equivalents for the Brownian motion in Holder norm. Probab. Th. Rel. Fields 93 457-484. MR 94a:60117
    • (1992) Probab. Th. Rel. Fields , vol.93 , pp. 457-484
    • Baldi, P.1    Roynette, B.2
  • 6
    • 84968502795 scopus 로고
    • On the maximum partial sums of sequences of independent random variables
    • MR 10:132b
    • Chung, K.L. (1948). On the maximum partial sums of sequences of independent random variables. Trans. Amer. Math. Soc. 64 205-233. MR 10:132b
    • (1948) Trans. Amer. Math. Soc. , vol.64 , pp. 205-233
    • Chung, K.L.1
  • 8
    • 0038094849 scopus 로고
    • Fubini's theorem for double Wiener integrals and the variance of the Brownian path
    • MR 92m:60072
    • Donati-Martin, C. and Yor, M. (1991). Fubini's theorem for double Wiener integrals and the variance of the Brownian path. Ann. Inst. H. Poincaré Probab. Statist. 27 181-200. MR 92m:60072
    • (1991) Ann. Inst. H. Poincaré Probab. Statist. , vol.27 , pp. 181-200
    • Donati-Martin, C.1    Yor, M.2
  • 9
    • 0000312121 scopus 로고
    • Sample functions of stochastic processes with stationary, independent increments
    • Dekker, New York. MR 53:4240
    • Fristedt, B.E. (1974). Sample functions of stochastic processes with stationary, independent increments. Adv. Probab. 3 241-396. Dekker, New York. MR 53:4240
    • (1974) Adv. Probab. , vol.3 , pp. 241-396
    • Fristedt, B.E.1
  • 10
    • 0001782008 scopus 로고
    • Probability theory: Its role and its impact
    • MR 27:1972
    • Kac, M. (1962). Probability theory: its role and its impact. SIAM Rev. 4 1-11. MR 27:1972
    • (1962) SIAM Rev. , vol.4 , pp. 1-11
    • Kac, M.1
  • 11
    • 0011645698 scopus 로고    scopus 로고
    • Levy-classes and self-normalization
    • paper no.l, MR 97h:60024
    • Khoshnevisan, D. (1996). Levy-classes and self-normalization. Electronic J. Probab. 1, paper no.l, 1-18. MR 97h:60024
    • (1996) Electronic J. Probab. , vol.1 , pp. 1-18
    • Khoshnevisan, D.1
  • 12
    • 0038433684 scopus 로고
    • Calculation of characteristic functions of some functionals of a Wiener process and a Brownian bridge (English translation)
    • MR 88f:60145
    • Klyachko, A.A. and Solodyannikov, Yu.V. (1987). Calculation of characteristic functions of some functionals of a Wiener process and a Brownian bridge (English translation). Th. Probab. Appl. 31 500-504. MR 88f:60145
    • (1987) Th. Probab. Appl. , vol.31 , pp. 500-504
    • Klyachko, A.A.1    Solodyannikov, Y.V.2
  • 13
    • 0011525850 scopus 로고
    • Local variation of diffusion in local time
    • MR 53:1754
    • Knight, F.B. (1973). Local variation of diffusion in local time. Ann. Probab. 1 1026-1034. MR 53:1754
    • (1973) Ann. Probab. , vol.1 , pp. 1026-1034
    • Knight, F.B.1
  • 14
    • 0031518992 scopus 로고    scopus 로고
    • A note on the long time asymptotics of the Brownian motion with applications to the theory of quantum measurement
    • CMP 98:04
    • Kolokoltsov, V.N. (1997). A note on the long time asymptotics of the Brownian motion with applications to the theory of quantum measurement. Potential Anal. 7 759-764. CMP 98:04
    • (1997) Potential Anal. , vol.7 , pp. 759-764
    • Kolokoltsov, V.N.1
  • 15
    • 0000946488 scopus 로고
    • Small ball problems for Brownian motion and the Brownian sheet
    • MR 94h:60121
    • Kuelbs, J. and Li, W.V. (1993). Small ball problems for Brownian motion and the Brownian sheet. J. Theoretical Probab. 6 547-577. MR 94h:60121
    • (1993) J. Theoretical Probab. , vol.6 , pp. 547-577
    • Kuelbs, J.1    Li, W.V.2
  • 16
    • 0001461506 scopus 로고
    • Metric entropy and the small ball problem for Gaussian measures
    • MR 94j:60078
    • Kuelbs, J. and Li, W.V. (1993). Metric entropy and the small ball problem for Gaussian measures. J. Fund. Anal. 116 133-157. MR 94j:60078
    • (1993) J. Fund. Anal. , vol.116 , pp. 133-157
    • Kuelbs, J.1    Li, W.V.2
  • 17
    • 0013199932 scopus 로고
    • Small ball probabilities for Gaussian processes with stationary increments under Holder norms
    • MR 9Gb:60096
    • Kuelbs, J., Li, W.V. and Shao, Q.-M. (1995). Small ball probabilities for Gaussian processes with stationary increments under Holder norms. J. Theoretical Probab. 8 361-386. MR 9Gb:60096
    • (1995) J. Theoretical Probab. , vol.8 , pp. 361-386
    • Kuelbs, J.1    Li, W.V.2    Shao, Q.-M.3
  • 18
    • 0001211949 scopus 로고
    • Lim inf results for Gaussian samples and Chung's functional LIL
    • MR 96h:60047
    • Kuelbs, J., Li, W.V. and Talagrand, M. (1994). Lim inf results for Gaussian samples and Chung's functional LIL. Ann. Probab. 22 1879-1903. MR 96h:60047
    • (1994) Ann. Probab. , vol.22 , pp. 1879-1903
    • Kuelbs, J.1    Li, W.V.2    Talagrand, M.3
  • 20
    • 0031101104 scopus 로고    scopus 로고
    • First exit time from a bounded interval for integrated Brownian motion
    • MR 98a:G0116
    • Lâchai, A. (1997). First exit time from a bounded interval for integrated Brownian motion. C. R. Acad. Sei. Paris. Sér. I Math. 324 559-564. MR 98a:G0116
    • (1997) C. R. Acad. Sei. Paris. Sér. I Math. , vol.324 , pp. 559-564
    • Lâchai, A.1
  • 22
    • 0001173694 scopus 로고
    • Comparison results for the lower tail of Gaussian seminorms
    • MR 93k:60088
    • Li, W.V. (1992). Comparison results for the lower tail of Gaussian seminorms. J. Theoretical Probab. 5 1-31. MR 93k:60088
    • (1992) J. Theoretical Probab. , vol.5 , pp. 1-31
    • Li, W.V.1
  • 24
    • 0000230359 scopus 로고
    • A winding problem for a resonator driven by a white noise
    • MR 27:6312
    • McKean, H.P. (1963). A winding problem for a resonator driven by a white noise. J. Math. Kyoto Univ. 2 227-235. MR 27:6312
    • (1963) J. Math. Kyoto Univ. , vol.2 , pp. 227-235
    • McKean, H.P.1
  • 26
    • 84939730902 scopus 로고
    • Mathematical analysis of random noise
    • MR G:89b
    • Rice, S.O. (1944). Mathematical analysis of random noise. Bell Syst. Techn. J. 23 282-332. MR G:89b
    • (1944) Bell Syst. Techn. J. , vol.23 , pp. 282-332
    • Rice, S.O.1
  • 27
    • 21844487711 scopus 로고
    • Small ball probabilities of Gaussian fields
    • MR 96h:60069
    • Shao, Q.-M. and Wang, D. (1995). Small ball probabilities of Gaussian fields. Probab. Th. Rel. Fields 102 511-517. MR 96h:60069
    • (1995) Probab. Th. Rel. Fields , vol.102 , pp. 511-517
    • Shao, Q.-M.1    Wang, D.2
  • 28
    • 21444453887 scopus 로고    scopus 로고
    • (199G). Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times
    • MR 98b:60076
    • Shi, Z. (199G). Small ball probabilities for a Wiener process under weighted sup-norms, with an application to the supremum of Bessel local times. J. Theoretical Probab. 9 915-929. MR 98b:60076
    • J. Theoretical Probab. , vol.9 , pp. 915-929
    • Shi, Z.1
  • 30
    • 21344456608 scopus 로고    scopus 로고
    • Some small ball probabilities for Gaussian processes under non-uniform norms
    • MR 97h:60036
    • Stolz, W. (1996). Some small ball probabilities for Gaussian processes under non-uniform norms. J. Theoretical Probab. 9 613-630. MR 97h:60036
    • (1996) J. Theoretical Probab. , vol.9 , pp. 613-630
    • Stolz, W.1
  • 31
    • 0000251720 scopus 로고
    • The small ball problem for the Brownian sheet
    • MR 95k:60049
    • Talagrand, M. (1994). The small ball problem for the Brownian sheet. Ann. Probab. 22 1331-1354. MR 95k:60049
    • (1994) Ann. Probab. , vol.22 , pp. 1331-1354
    • Talagrand, M.1
  • 32
    • 0000683728 scopus 로고
    • A property of Brownian motion paths
    • MR 20:2795
    • Trotter, H.F. (1958). A property of Brownian motion paths. Illinois J. Math. 2 425-433. MR 20:2795
    • (1958) Illinois J. Math. , vol.2 , pp. 425-433
    • Trotter, H.F.1
  • 33
    • 33847689666 scopus 로고
    • Some Aspects of Brownian Motion
    • Birkhäuser, Basel. MR 93i:60155
    • Yor, M. (1992). Some Aspects of Brownian Motion. Part I: Some Special Functionals. Birkhäuser, Basel. MR 93i:60155
    • (1992) Part I: some Special Functionals.
    • Yor, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.