메뉴 건너뛰기




Volumn 206, Issue 3, 2011, Pages 211-271

Spectral analysis of subordinate Brownian motions on the half-line

Author keywords

Complete Bernstein function; First passage time; Half line; Killed process; L vy process; Spectral theory; Subordination

Indexed keywords


EID: 82755165257     PISSN: 00393223     EISSN: None     Source Type: Journal    
DOI: 10.4064/sm206-3-2     Document Type: Article
Times cited : (46)

References (75)
  • 2
    • 2942668409 scopus 로고    scopus 로고
    • The Cauchy process and the Steklov problem
    • DOI 10.1016/j.jfa.2004.02.005
    • R. Bañuelos and T. Kulczycki, The Cauchy process and the Steklov problem, J. Funct. Anal. 211 (2004), 355-423. (Pubitemid 38773471)
    • (2004) Journal of Functional Analysis , vol.211 , Issue.2 , pp. 355-423
    • Banuelos, R.1    Kulczycki, T.2
  • 3
    • 33750883367 scopus 로고    scopus 로고
    • Spectral gap for the cauchy process on convex, symmetric domains
    • DOI 10.1080/03605300600856188, PII W1141034647U4803
    • R. Bañuelos and T. Kulczycki, Spectral gap for the Cauchy process on convex symmetric domains, Comm. Partial Differential Equations 31 (2006), 1841-1878. (Pubitemid 44721724)
    • (2006) Communications in Partial Differential Equations , vol.31 , Issue.12 , pp. 1841-1878
    • Banuelos, R.1    Kulczycki, T.2
  • 4
    • 0010086233 scopus 로고
    • On the distribution of the supremum functional for processes with stationary independent increments
    • G. Baxter and M. D. Donsker, On the distribution of the supremum functional for processes with stationary independent increments, Trans. Amer. Math. Soc. 85 (1957), 73-87.
    • (1957) Trans. Amer. Math. Soc. , vol.85 , pp. 73-87
    • Baxter, G.1    Donsker, M.D.2
  • 5
    • 0003975247 scopus 로고    scopus 로고
    • Cambridge Univ. Press Melbourne-New York
    • J. Bertoin, Lévy Processes, Cambridge Univ. Press, Melbourne-New York, 1998.
    • (1998) Lévy Processes
    • Bertoin, J.1
  • 8
    • 0002020384 scopus 로고    scopus 로고
    • Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
    • K. Bogdan and T. Byczkowski, Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains, Studia Math. 133 (1999), 53-92.
    • (1999) Studia Math. , vol.133 , pp. 53-92
    • Bogdan, K.1    Byczkowski, T.2
  • 9
    • 0041862067 scopus 로고    scopus 로고
    • Potential theory of Schrodinger operator based on fractional Laplacian
    • K. Bogdan and T. Byczkowski, Potential theory of Schrödinger operator based on fractional Laplacian, Probab. Math. Statist. 20 (2000), 293-335. (Pubitemid 33313655)
    • (2000) Probability and Mathematical Statistics , vol.20 , Issue.2 , pp. 293-335
    • Bogdan, K.1    Byczkowski, T.2
  • 11
    • 77957229988 scopus 로고    scopus 로고
    • Heat kernel estimates for the fractional Laplacian
    • K. Bogdan, T. Grzywny and M. Ryznar, Heat kernel estimates for the fractional Laplacian, Ann. Probab. 38 (2010), 1901-1923.
    • (2010) Ann. Probab. , vol.38 , pp. 1901-1923
    • Bogdan, K.1    Grzywny, T.2    Ryznar, M.3
  • 12
    • 68749083442 scopus 로고    scopus 로고
    • Bessel potentials, hitting distributions and Green functions
    • T. Byczkowski, J. Malecki and M. Ryznar, Bessel potentials, hitting distributions and Green functions, Trans. Amer. Math. Soc. 361 (2009), 4871-4900.
    • (2009) Trans. Amer. Math. Soc. , vol.361 , pp. 4871-4900
    • Byczkowski, T.1    Malecki, J.2    Ryznar, M.3
  • 13
    • 77952292884 scopus 로고    scopus 로고
    • Hitting half-spaces by Bessel-Brownian diffusions
    • T. Byczkowski, J. Malecki, Hitting half-spaces by Bessel-Brownian diffusions, Potential Anal. 33 (2010), 47-83.
    • (2010) Potential Anal. , vol.33 , pp. 47-83
    • Byczkowski, T.1    Malecki, J.2
  • 14
    • 84861345147 scopus 로고    scopus 로고
    • Sharp heat kernel estimates for relativistic stable processes in open sets
    • to appear
    • Z. Q. Chen, P. Kim and R. Song, Sharp heat kernel estimates for relativistic stable processes in open sets, Ann. Probab., to appear.
    • Ann. Probab.
    • Chen, Z.Q.1    Kim, P.2    Song, R.3
  • 15
    • 0031572650 scopus 로고    scopus 로고
    • Intrinsic ultracontractivity and conditional gauge for symmetric stable processes
    • DOI 10.1006/jfan.1997.3104, PII S0022123697931049
    • Z. Q. Chen and R. Song, Intrinsic ultracontractivity and conditional gauge for symmetric stable processes, J. Funct. Anal. 150 (1997) 204-239. (Pubitemid 127175026)
    • (1997) Journal of Functional Analysis , vol.150 , Issue.1 , pp. 204-239
    • Chen, Z.-Q.1    Song, R.2
  • 17
    • 76349103203 scopus 로고    scopus 로고
    • Spectral properties of subordinate processes in domains
    • Stochastic Analysis and Partial Differential Equations, G.-Q. Chen et al. (eds.)
    • Z. Q. Chen and R. Song, Spectral properties of subordinate processes in domains, in: Stochastic Analysis and Partial Differential Equations,G.-Q. Chen et al. (eds.), Contemp. Math. 429, Amer. Math. Soc., 2007, 77-84.
    • (2007) Contemp. Math. 429, Amer. Math. Soc. , pp. 77-84
    • Chen, Z.Q.1    Song, R.2
  • 18
    • 0010667599 scopus 로고
    • Doubly-Feller process with multiplicative functional
    • Seminar on Stochastic Processes 1985 (Gainesville, FL 1985) Birkhäuser, Boston, Boston, MA
    • K. L. Chung, Doubly-Feller process with multiplicative functional, in: Seminar on Stochastic Processes, 1985 (Gainesville, FL, 1985), Progr. Probab. Statist. 12, Birkhäuser, Boston, Boston, MA, 1986, 63-78.
    • (1986) Progr. Probab. Statist. , vol.12 , pp. 63-78
    • Chung, K.L.1
  • 19
    • 2942634534 scopus 로고
    • The first exit time of a two-dimensional symmetric stable process from a wedge
    • R. D. DeBlassie, The first exit time of a two-dimensional symmetric stable process from a wedge, Ann. Probab. 18 (1990), 1034-1070.
    • (1990) Ann. Probab. , vol.18 , pp. 1034-1070
    • De Blassie, R.D.1
  • 20
    • 4043135243 scopus 로고    scopus 로고
    • Higher order PDEs and symmetric stable processes
    • R. D. DeBlassie, Higher order PDE's and symmetric stable processes, Probab. Theory Related Fields 129 (2004), 495-536. (Pubitemid 39056960)
    • (2004) Probability Theory and Related Fields , vol.129 , Issue.4 , pp. 495-536
    • DeBlassie, R.D.1
  • 21
    • 34547341496 scopus 로고    scopus 로고
    • α-continuity properties of the symmetric α-stable process
    • R. D. DeBlassie and P. J. Méndez-Hernández, α-continuity properties of the symmetric α-stable process, Trans. Amer. Math. Soc. 359 (2007), 2343-2359.
    • (2007) Trans. Amer. Math. Soc. , vol.359 , pp. 2343-2359
    • De Blassie, R.D.1    Méndez-Hernández, P.J.2
  • 22
    • 0010115452 scopus 로고
    • Convolution and S0-convolution of distributions
    • P. Dierolf and J. Voigt, Convolution and S0-convolution of distributions, Collect. Math. 29 (1978), 185-196.
    • (1978) Collect. Math. , vol.29 , pp. 185-196
    • Dierolf, P.1    Voigt, J.2
  • 24
    • 77953675815 scopus 로고    scopus 로고
    • The asymptotic behavior of densities related to the supremum of a stable process
    • R. A. Doney and M. S. Savov, The asymptotic behavior of densities related to the supremum of a stable process, Ann. Probab. 38 (2010), 316-326.
    • (2010) Ann. Probab. , vol.38 , pp. 316-326
    • Doney, R.A.1    Savov, M.S.2
  • 26
    • 55849138398 scopus 로고    scopus 로고
    • Variational methods in relativistic quantum mechanics
    • M. J. Esteban, M. Lewin and E. Séré, Variational methods in relativistic quantum mechanics, Bull. Amer. Math. Soc. 45 (2008), 545-593.
    • (2008) Bull. Amer. Math. Soc. , vol.45 , pp. 545-593
    • Esteban, M.J.1    Lewin, M.2    Séré, E.3
  • 29
    • 0002154052 scopus 로고
    • Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics
    • P. Garbaczewski, J. R. Klauder and R. Olkiewicz, Schrödinger problem, Lévy processes, and noise in relativistic quantum mechanics, Phys. Rev. E 51 (1995), 4114-4131.
    • (1995) Phys. Rev. E , vol.51 , pp. 4114-4131
    • Garbaczewski, P.1    Klauder, J.R.2    Olkiewicz, R.3
  • 30
    • 84972514239 scopus 로고
    • Markov operators and their associated semi-groups
    • R. K. Getoor, Markov operators and their associated semi-groups, Pacific J. Math. 9 (1959), 449-472.
    • (1959) Pacific J. Math. , vol.9 , pp. 449-472
    • Getoor, R.K.1
  • 34
    • 0010172001 scopus 로고
    • On the exchange formula for distributions
    • Y. Hirata and H. Ogata, On the exchange formula for distributions, J. Sci. Hiroshima Univ. Ser. A 22 (1958), 147-152.
    • (1958) J. Sci. Hiroshima Univ. Ser. A , vol.22 , pp. 147-152
    • Hirata, Y.1    Ogata, H.2
  • 35
    • 64249155094 scopus 로고    scopus 로고
    • On the first passage time for Brownian motion subordinated by a Lévy process
    • T. R. Hurd and A. Kuznetsov, On the first passage time for Brownian motion subordinated by a Lévy process, J. Appl. Probab. 46 (2009), 181-198.
    • (2009) J. Appl. Probab. , vol.46 , pp. 181-198
    • Hurd, T.R.1    Kuznetsov, A.2
  • 36
    • 79958169886 scopus 로고    scopus 로고
    • Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Lévy processes
    • Y. Isozaki, Hitting of a line or a half-line in the plane by two-dimensional symmetric stable Lévy processes, Stoch. Process. Appl. 121 (2011), 1749-1769.
    • (2011) Stoch. Process. Appl. , vol.121 , pp. 1749-1769
    • Isozaki, Y.1
  • 39
    • 0040059800 scopus 로고
    • Convolution, product and Fourier transform of distributions
    • A. Kamiński, Convolution, product and Fourier transform of distributions, Studia Math. 74 (1982), 83-96.
    • (1982) Studia Math. , vol.74 , pp. 83-96
    • Kamiński, A.1
  • 40
    • 62249180786 scopus 로고    scopus 로고
    • Boundary Harnack principle for subordinate Brownian motions
    • P. Kim, R. Song and Z. Vondraček, Boundary Harnack principle for subordinate Brownian motions, Stoch. Process. Appl. 119 (2009), 1601-1631.
    • (2009) Stoch. Process. Appl. , vol.119 , pp. 1601-1631
    • Kim, P.1    Song, R.2    Vondraček, Z.3
  • 41
    • 77954089169 scopus 로고    scopus 로고
    • On the potential theory of one-dimensional subordinate Brownian motions with continuous components
    • P. Kim, R. Song and Z. Vondraček, On the potential theory of one-dimensional subordinate Brownian motions with continuous components, Potential Anal. 33 (2010), 153-173.
    • (2010) Potential Anal. , vol.33 , pp. 153-173
    • Kim, P.1    Song, R.2    Vondraček, Z.3
  • 42
    • 80052957258 scopus 로고    scopus 로고
    • On harmonic functions for trace processes
    • P. Kim, R. Song and Z. Vondraček, On harmonic functions for trace processes, Math. Nachr. 284 (2011), 1889-1902.
    • (2011) Math. Nachr. , vol.284 , pp. 1889-1902
    • Kim, P.1    Song, R.2    Vondraček, Z.3
  • 45
    • 0000105945 scopus 로고
    • Krein's spectral theory of strings and generalized diffusion processes in: Functional analysis in markov processes (Katata/Kyoto)
    • Springer, Berlin 1981
    • S. Kotani and S. Watanabe, Krein's spectral theory of strings and generalized diffusion processes, in: Functional Analysis in Markov processes (Katata/Kyoto, 1981), Lecture Notes in Math. 923, Springer, Berlin, 1982, 235-259.
    • (1982) Lecture Notes in Math. , vol.923 , pp. 235-259
    • Kotani, S.1    Watanabe, S.2
  • 46
    • 0006089566 scopus 로고
    • Integral equations on a half-line with kernel depending upon the difference of the arguments
    • M. G. Kre.in, Integral equations on a half-line with kernel depending upon the difference of the arguments, Transl. Amer. Math. Soc. (2) 22 (1962), 163-288; transl.
    • (1962) Transl. Amer. Math. Soc. , vol.22 , Issue.2 , pp. 163-288
    • Kre, M.G.1
  • 47
    • 82755162194 scopus 로고
    • Transl. from Uspekhi Mat. Nauk 13 (1958), no. 5, 3-120.
    • (1958) Uspekhi Mat. Nauk , vol.13 , Issue.5 , pp. 3-120
  • 48
    • 0002345448 scopus 로고    scopus 로고
    • Properties of Green function of symmetric stable processes
    • T. Kulczycki, Properties of Green function of symmetric stable processes, Probab. Math. Statist. 17 (1997), 339-364. (Pubitemid 128087871)
    • (1997) Probability and Mathematical Statistics , vol.17 , Issue.2 , pp. 339-364
    • Kulczycki, T.1
  • 49
    • 0038434657 scopus 로고    scopus 로고
    • Intrinsic ultracontractivity for symmetric stable processes
    • T. Kulczycki, Intrinsic ultracontractivity for symmetric stable processes, Bull. Polish Acad. Sci. Math. 46 (1998), 325-334.
    • (1998) Bull. Polish Acad. Sci. Math. , vol.46 , pp. 325-334
    • Kulczycki, T.1
  • 50
  • 51
    • 33750166957 scopus 로고    scopus 로고
    • Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes
    • DOI 10.1090/S0002-9947-06-03931-6, PII S0002994706039316
    • T. Kulczycki and B. Siudeja, Intrinsic ultracontractivity of the Feynman-Kac semigroup for relativistic stable processes, Trans. Amer. Math. Soc. 358 (2006), 5025-5057. (Pubitemid 44598810)
    • (2006) Transactions of the American Mathematical Society , vol.358 , Issue.11 , pp. 5025-5057
    • Kulczycki, T.1    Siudeja, B.2
  • 52
    • 79953133693 scopus 로고    scopus 로고
    • On extrema of stable processes
    • A. Kuznetsov, On extrema of stable processes, Ann. Probab. 39 (2011), 1027-1060.
    • Ann. Probab. , vol.39 , Issue.2011 , pp. 1027-1060
    • Kuznetsov, A.1
  • 54
    • 82755162193 scopus 로고    scopus 로고
    • Spectral analysis of subordinate brownian motions in half-line
    • arXiv:1006.0524v1
    • M. Kwaśnicki, Spectral analysis of subordinate Brownian motions in half-line. Preliminary version, arXiv:1006.0524v1, 2010.
    • (2010) Preliminary Version
    • Kwaśnicki, M.1
  • 60
    • 0000944515 scopus 로고
    • Symmetric stable processes as traces of degenerate diffusion processes
    • S. A. Molchanov and E. Ostrovskiǐ, Symmetric stable processes as traces of degenerate diffusion processes, Theor. Probab. Appl. 14 (1969), 128-131.
    • (1969) Theor. Probab. Appl. , vol.14 , pp. 128-131
    • Molchanov, S.A.1    Ostrovskiǐ, E.2
  • 62
    • 0000728524 scopus 로고
    • Expansions in generalized eigenfunctions of selfadjoint operators
    • T. Poerschke, G. Stolz and J. Weidmann, Expansions in generalized eigenfunctions of selfadjoint operators, Math. Z. 202 (1989), 397-408.
    • (1989) Math. Z. , vol.202 , pp. 397-408
    • Poerschke, T.1    Stolz, G.2    Weidmann, J.3
  • 63
    • 47749112382 scopus 로고
    • Wiener-Hopf factorization of diffusions and Lévy processes
    • L. C. G. Rogers, Wiener-Hopf factorization of diffusions and Lévy processes, Proc. London Math. Soc. 47 (1983), 177-191.
    • (1983) Proc. London Math. Soc. , vol.47 , pp. 177-191
    • Rogers, L.C.G.1
  • 64
    • 0036251925 scopus 로고    scopus 로고
    • Estimates of Green function for relativistic α-stable process
    • DOI 10.1023/A:1015231913916
    • M. Ryznar, Estimates of Green function for relativistic α-stable process, Potential Anal. 17 (2002), 1-23. (Pubitemid 37132662)
    • (2002) Potential Analysis , vol.17 , Issue.1 , pp. 1-23
    • Ryznar, M.1
  • 67
    • 84972534216 scopus 로고
    • On the multiplicative products of distributions
    • R. Shiraishi and M. Itano, On the multiplicative products of distributions, J. Sci. Hiroshima Univ. Ser. A 28 (1964), 223-235.
    • (1964) J. Sci. Hiroshima Univ. Ser. A , vol.28 , pp. 223-235
    • Shiraishi, R.1    Itano, M.2
  • 68
    • 85016600983 scopus 로고
    • Schrödinger semigroups
    • B. Simon, Schrödinger semigroups, Bull. Amer. Math. Soc. 7 (1982), 447-526.
    • (1982) Bull. Amer. Math. Soc. , vol.7 , pp. 447-526
    • Simon, B.1
  • 69
    • 33845666586 scopus 로고    scopus 로고
    • Potential theory of special subordinators and subordinate killed stable processes
    • DOI 10.1007/s10959-006-0045-y
    • R. Song and Z. Vondraček, Potential theory of special subordinators and subordinate killed stable processes, J. Theoret. Probab. 19 (2006), 817-847. (Pubitemid 44953096)
    • (2006) Journal of Theoretical Probability , vol.19 , Issue.4 , pp. 817-847
    • Song, R.1    Vondracek, Z.2
  • 70
    • 45849111898 scopus 로고    scopus 로고
    • On the relationship between subordinate killed and killed subordinate processes
    • R. Song and Z. Vondraček, On the relationship between subordinate killed and killed subordinate processes, Electron. Comm. Probab. 13 (2008), 325-336.
    • (2008) Electron. Comm. Probab. , vol.13 , pp. 325-336
    • Song, R.1    Vondraček, Z.2
  • 71
    • 84927465241 scopus 로고
    • Some theorems concerning 2-dimensional Brownian motion
    • F. Spitzer, Some theorems concerning 2-dimensional Brownian motion, Trans. Amer. Math. Soc. 87 (1958), 187-197.
    • (1958) Trans. Amer. Math. Soc. , vol.87 , pp. 187-197
    • Spitzer, F.1
  • 74
    • 0039878157 scopus 로고
    • reprinted in Norbert Wiener MIT Press, Cambridge, MA
    • reprinted in Norbert Wiener: Collected Works MIT Press, Cambridge, MA,3,1981.
    • (1981) Collected Works , vol.3
  • 75
    • 34548175480 scopus 로고    scopus 로고
    • Fractional laplacian in bounded domains
    • A. Zoia, A. Rosso and M. Kardar, Fractional Laplacian in bounded domains, Phys. Rev. E 76 (2007), 061121.
    • (2007) Phys. Rev. E , vol.76 , pp. 061121
    • Zoia, A.1    Rosso, A.2    Kardar, M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.