메뉴 건너뛰기




Volumn 104, Issue 2, 2003, Pages 193-216

Local times of additive Lévy processes

Author keywords

Additive and strictly stable L vy processes; Laws of the iterated logarithm; Local and uniform H lder estimates; Local times

Indexed keywords


EID: 0037399057     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00237-5     Document Type: Article
Times cited : (31)

References (41)
  • 2
    • 0013252913 scopus 로고
    • Continuity of local times for Lévy processes
    • Barlow, M.T., 1985. Continuity of local times for Lévy processes. Z. Wahrsch. Verw. Gebiete 69, 3-35.
    • (1985) Z. Wahrsch. Verw. Gebiete , vol.69 , pp. 3-35
    • Barlow, M.T.1
  • 3
    • 0003007390 scopus 로고
    • Necessary and sufficient conditions for the continuity of local time of Lévy processes
    • Barlow, M.T., 1988. Necessary and sufficient conditions for the continuity of local time of Lévy processes. Ann. Probab. 16, 1389-1427.
    • (1988) Ann. Probab. , vol.16 , pp. 1389-1427
    • Barlow, M.T.1
  • 4
    • 0013252792 scopus 로고
    • Application de l'entropie métrique à la continuité des temps locaux des processus de Lévy
    • Barlow, M.T., Hawkes, J., 1985. Application de l'entropie métrique à la continuité des temps locaux des processus de Lévy. C. R. Acad. Sci. Paris Sér. I Math. 301, 237-239.
    • (1985) C. R. Acad. Sci. Paris Sér. I Math. , vol.301 , pp. 237-239
    • Barlow, M.T.1    Hawkes, J.2
  • 5
    • 84972535818 scopus 로고
    • Gaussian sample function: Uniform dimension and Hölder conditions nowhere
    • Berman, S.M., 1972. Gaussian sample function: uniform dimension and Hölder conditions nowhere. Nagoya Math. J. 46, 63-86.
    • (1972) Nagoya Math. J. , vol.46 , pp. 63-86
    • Berman, S.M.1
  • 6
    • 0004044694 scopus 로고    scopus 로고
    • Lévy Processes
    • Cambridge University Press, Cambridge
    • Bertoin, J., 1996. Lévy Processes. Cambridge University Press, Cambridge.
    • (1996)
    • Bertoin, J.1
  • 7
    • 0000361942 scopus 로고
    • Sample functions of stochastic processes with stationary independent increments
    • Blumenthal, R.M., Getoor, R.K., 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.K.2
  • 9
    • 21144462388 scopus 로고
    • Geography of the level sets of the Brownian sheet
    • Dalang, R.C., Walsh, J.B., 1993a. Geography of the level sets of the Brownian sheet. Probab. Theory Related Fields 96 (2), 153-176.
    • (1993) Probab. Theory Related Fields , vol.96 , Issue.2 , pp. 153-176
    • Dalang, R.C.1    Walsh, J.B.2
  • 11
    • 84980138040 scopus 로고
    • On laws of the iterated logarithm for local times
    • Donsker, M.D., Varadhan, S.R.S., 1977. On laws of the iterated logarithm for local times. Comm. Pure Appl. Math. 30, 707-753.
    • (1977) Comm. Pure Appl. Math. , vol.30 , pp. 707-753
    • Donsker, M.D.1    Varadhan, S.R.S.2
  • 12
    • 0001287276 scopus 로고
    • Sample function properties of the multi-parameter stable process
    • Ehm, W., 1981. Sample function properties of the multi-parameter stable process. Z. Wahrsch. Verw. Gebiete 56, 195-228.
    • (1981) Z. Wahrsch. Verw. Gebiete , vol.56 , pp. 195-228
    • Ehm, W.1
  • 15
  • 16
    • 0001854055 scopus 로고
    • A local time analysis of intersection of Brownian paths in the space
    • Geman, D., Horowitz, J., Rosen, J., 1984. A local time analysis of intersection of Brownian paths in the space. Ann. Probab. 12, 86-107.
    • (1984) Ann. Probab. , vol.12 , pp. 86-107
    • Geman, D.1    Horowitz, J.2    Rosen, J.3
  • 17
    • 0000158981 scopus 로고
    • Continuity of local times for Markov processes
    • Getoor, R.K., Kesten, H., 1972. Continuity of local times for Markov processes. Comput. Math. 24, 277-303.
    • (1972) Comput. Math. , vol.24 , pp. 277-303
    • Getoor, R.K.1    Kesten, H.2
  • 18
    • 0003543733 scopus 로고
    • Cambridge University Press, Cambridge
    • Hardy, G.H., 1934. Inequalities. Cambridge University Press, Cambridge.
    • (1934) Inequalities
    • Hardy, G.H.1
  • 19
    • 29144503868 scopus 로고
    • Local times as stationary processes
    • Elworthy, K.D. (Ed.), Pitman Research Notes in Mathematics Longman, Chicago
    • Hawkes, J., 1986. Local times as stationary processes. In: Elworthy, K.D. (Ed.), From Local Times to Global Geometry. Pitman Research Notes in Mathematics, Vol. 150. Longman, Chicago, pp. 111-120.
    • (1986) From Local Times to Global Geometry , vol.150 , pp. 111-120
    • Hawkes, J.1
  • 20
    • 21844493266 scopus 로고
    • Symmetric Skorohod topology on n-variable functions and hierarchical Markov properties of n-parameter processes
    • Hirsch, F., Song, S., 1995. 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
  • 21
    • 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
  • 23
    • 0000307340 scopus 로고
    • Contours of Brownian processes with several-dimensional times
    • Kendall, W.S., 1980. Contours of Brownian processes with several-dimensional times. Z. Wahr. Verw. Geb. 52, 267-276.
    • (1980) Z. Wahr. Verw. Geb. , vol.52 , pp. 267-276
    • Kendall, W.S.1
  • 24
    • 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
  • 25
    • 22644448542 scopus 로고    scopus 로고
    • Brownian sheet images and Bessel-Riesz. capacity
    • Khoshnevisan, D., 1999. Brownian sheet images and Bessel-Riesz capacity. Trans. Amer. Math. Soc. 351 (7), 2607-2622.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , Issue.7 , pp. 2607-2622
    • Khoshnevisan, D.1
  • 26
    • 0033164051 scopus 로고    scopus 로고
    • Brownian sheet and capacity
    • Khoshnevisan, D., Shi, Z., 1999. Brownian sheet and capacity. Ann. Probab. 27, 1135-1159.
    • (1999) Ann. Probab. , vol.27 , pp. 1135-1159
    • Khoshnevisan, D.1    Shi, Z.2
  • 27
    • 0013249791 scopus 로고    scopus 로고
    • Level sets of additive random walks
    • Giné, E., Mason, D.M., Wellner, J.A. (Eds.), (Seattle, 1999), Progress in Probability, BirkhBauser, Basel
    • Khoshnevisan, D., Xiao, Y., 2000. Level sets of additive random walks. In: Giné, E., Mason, D.M., Wellner, J.A. (Eds.), High Dimensional Probability (Seattle, 1999), Progress in Probability, Vol. 47. BirkhBauser, Basel, pp. 329-345.
    • (2000) High Dimensional Probability , vol.47 , pp. 329-345
    • Khoshnevisan, D.1    Xiao, Y.2
  • 28
    • 0035993022 scopus 로고    scopus 로고
    • Level sets of additive Lévy process
    • Khoshnevisan, D., Xiao, Y., 2002. Level sets of additive Lévy process. Ann. Probab. 30, 62-100.
    • (2002) Ann. Probab. , vol.30 , pp. 62-100
    • Khoshnevisan, D.1    Xiao, Y.2
  • 29
    • 0013313864 scopus 로고    scopus 로고
    • On the explosion of the local times of Brownian sheet along lines
    • Preprint
    • Khoshnevisan, D., Révész, P., Shi, Z., 2001. On the explosion of the local times of Brownian sheet along lines, Preprint.
    • (2001)
    • Khoshnevisan, D.1    Révész, P.2    Shi, Z.3
  • 30
    • 0013252794 scopus 로고    scopus 로고
    • Measuring the range of an additive Lévy process
    • to appear
    • Khoshnevisan, D., Xiao, Y., Zhong, Y., 2002. Measuring the range of an additive Lévy process. Ann. Probab., to appear.
    • (2002) Ann. Probab.
    • Khoshnevisan, D.1    Xiao, Y.2    Zhong, Y.3
  • 31
    • 0013268139 scopus 로고
    • Limit laws for local times of the Brownian sheet
    • Lacey, M.T., 1990. Limit laws for local times of the Brownian sheet. Probab. Theory Related Fields 86, 63-85.
    • (1990) Probab. Theory Related Fields , vol.86 , pp. 63-85
    • Lacey, M.T.1
  • 32
  • 33
    • 0000292544 scopus 로고
    • Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes
    • Marcus, M.B., Rosen, J., 1992. Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes. Ann. Probab. 20, 1603-1684.
    • (1992) Ann. Probab. , vol.20 , pp. 1603-1684
    • Marcus, M.B.1    Rosen, J.2
  • 34
    • 0002672495 scopus 로고
    • Local nondeterminism and Hausdorff dimension
    • Ci̧nlar, E., Chung, K.L., Getoor, R.K. (Eds.), Birkhauser, Basel
    • Monrad, D., Pitt, L.D., 1987. Local nondeterminism and Hausdorff dimension. In: Ci̧nlar, E., Chung, K.L., Getoor, R.K. (Eds.), Progress in Probability and Statistics, Seminar on Stochastic Processes (1986). Birkhauser, Basel, pp. 163-189.
    • (1986) Progress in Probability and Statistics, Seminar on Stochastic Processes , pp. 163-189
    • Monrad, D.1    Pitt, L.D.2
  • 35
    • 0030519891 scopus 로고    scopus 로고
    • Packing and covering indices for a general Lévy process
    • Pruitt, W.E., 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
  • 36
    • 0000418064 scopus 로고
    • Self-intersection of random fields
    • Rosen, J., 1984. Self-intersection of random fields. Ann. Probab. 12, 108-119.
    • (1984) Ann. Probab. , vol.12 , pp. 108-119
    • Rosen, J.1
  • 38
    • 0000251720 scopus 로고
    • The small ball problem for the Brownian sheet
    • Talagrand, M., 1994. The small ball problem for the Brownian sheet. Ann. Probab. 22, 1331-1354.
    • (1994) Ann. Probab. , vol.22 , pp. 1331-1354
    • Talagrand, M.1
  • 39
    • 0001299350 scopus 로고
    • Sample path properties of a transient stable process
    • Taylor, S.J., 1967. Sample path properties of a transient stable process. J. Math. Mech. 16, 1229-1246.
    • (1967) J. Math. Mech. , vol.16 , pp. 1229-1246
    • Taylor, S.J.1
  • 40
    • 0013270032 scopus 로고
    • Local times for two-parameter Lev́y processes
    • Vares, M.E., 1983. Local times for two-parameter Lev́y processes. Stochastic Process. Appl. 15, 59-82.
    • (1983) Stochastic Process. Appl. , vol.15 , pp. 59-82
    • Vares, M.E.1
  • 41
    • 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. Probab. Theory Related Fields 109, 129-157.
    • (1997) Probab. Theory Related Fields , vol.109 , pp. 129-157
    • Xiao, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.