메뉴 건너뛰기




Volumn s3-65, Issue 2, 1992, Pages 326-356

Arcsine laws and interval partitions derived from a stable subordinator

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84962993911     PISSN: 00246115     EISSN: 1460244X     Source Type: Journal    
DOI: 10.1112/plms/s3-65.2.326     Document Type: Article
Times cited : (100)

References (46)
  • 1
    • 0001396770 scopus 로고
    • On Walsh's Brownian motions
    • Lecture Notes in Mathematics 1372 (Springer, Berlin)
    • M. Barlow, J. Pitman, and M. Yor, On Walsh's Brownian motions;, Séminaire de Probabilités XXlll, Lecture Notes in Mathematics 1372 (Springer, Berlin, 1989), pp. 275-293.
    • (1989) Séminaire de Probabilités XXlll , pp. 275-293
    • Barlow, M.1    Pitman, J.2    Yor, M.3
  • 2
    • 0001465651 scopus 로고
    • Une extension multidimensionnelle de la loi de l'arc sinus
    • Lecture Notes in Mathematics 1372 (Springer, Berlin)
    • M. Barlow, J. Pitman, and M. Yor, Une extension multidimensionnelle de la loi de l'arc sinus;, Séminaire de Probabilités XXlll, Lecture Notes in Mathematics 1372 (Springer, Berlin, 1989), pp. 294-314.
    • (1989) Séminaire de Probabilités XXlll , pp. 294-314
    • Barlow, M.1    Pitman, J.2    Yor, M.3
  • 3
    • 0039024636 scopus 로고
    • Un processus qui ressemble au pont Brownien
    • Lecture Notes in Mathematics 1247 (Springer, Berlin)
    • P. Biane, J. F. Le Gall, and M. Yor, Un processus qui ressemble au pont Brownien;, Séminaire de Probabilités XXI, Lecture Notes in Mathematics 1247 (Springer, Berlin, 1987), pp. 270-275.
    • (1987) Séminaire de Probabilités XXI , pp. 270-275
    • Biane, P.1    Le Gall, J.F.2    Yor, M.3
  • 4
    • 0042806303 scopus 로고
    • On higher-dimensional analogues of the arc-sine law
    • N. H. Bingham and R. A. Doney, On higher-dimensional analogues of the arc-sine law;, J. Appl. Probab. 25 (1988) 120-131.
    • (1988) J. Appl. Probab , vol.25 , pp. 120-131
    • Bingham, N.H.1    Doney, R.A.2
  • 5
    • 0002617436 scopus 로고
    • Ferguson distributions via Pòlya urn schemes
    • D. Blackwell and J. B. MacQueen, Ferguson distributions via Pòlya urn schemes;, Ann. Statist. 1 (1973) 353-355.
    • (1973) Ann. Statist , vol.1 , pp. 353-355
    • Blackwell, D.1    McQueen, J.B.2
  • 6
    • 0141630420 scopus 로고
    • Diffusions as a limit of stretched Brownian motions
    • J. K. Brooks and R. V. Chacon, Diffusions as a limit of stretched Brownian motions;, Adv. in Math. 49, No. 2 (1983) 109-122.
    • (1983) Adv. In Math , vol.49 , Issue.2 , pp. 109-122
    • Brooks, J.K.1    Chacon, R.V.2
  • 8
    • 38249024666 scopus 로고
    • Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex
    • P. Donnelly and P. Joyce, Continuity and weak convergence of ranked and size-biased permutations on the infinite simplex;, Stochastic Process. Appl. 31 (1989) 89-103.
    • (1989) Stochastic Process. Appl , vol.31 , pp. 89-103
    • Donnelly, P.1    Joyce, P.2
  • 9
    • 0007234226 scopus 로고
    • Some limit theorems for sums of independent random variables with infinite mathematical expectations
    • E. B. Dynkin, Some limit theorems for sums of independent random variables with infinite mathematical expectations;, 1MS-AMS Selected Trans. Math. Statist. Prob. 1 (1961) 171-189.
    • (1961) 1MS-AMS Selected Trans. Math. Statist. Prob , vol.1 , pp. 171-189
    • Dynkin, E.B.1
  • 10
    • 0002357984 scopus 로고
    • Population genetics theory-the past and the future
    • (ed. S. Lessard, University of Montreal Press)
    • W. J. Ewens, Population genetics theory-the past and the future;, Mathematical and statistical problems in evolution (ed. S. Lessard, University of Montreal Press, 1988), pp. 57-88.
    • (1988) Mathematical and statistical problems in evolution , pp. 57-88
    • Ewens, W.J.1
  • 11
    • 0001120413 scopus 로고
    • A Bayesian analysis of some nonparametric problems
    • T. S. Ferguson, A Bayesian analysis of some nonparametric problems;, Ann. Statist. 1 (1973) 209-230.
    • (1973) Ann. Statist , vol.1 , pp. 209-230
    • Ferguson, T.S.1
  • 13
    • 84911304212 scopus 로고
    • Produits semi-directs de diffusions réelles et lois asymptotiques
    • J. Franchi, Produits semi-directs de diffusions réelles et lois asymptotiques;, Adv. Appl. Probab. 21 (1989) 756-769.
    • (1989) Adv. Appl. Probab , vol.21 , pp. 756-769
    • Franchi, J.1
  • 14
    • 0007197086 scopus 로고
    • Excursions of a Markov process
    • R. K. Getoor, Excursions of a Markov process;, Ann. Probab. 1 (1979) 244-266.
    • (1979) Ann. Probab , vol.1 , pp. 244-266
    • Getoor, R.K.1
  • 15
    • 0001327573 scopus 로고
    • Fluctuation identities for Lévy processes and splitting at the maximum
    • P. Greenwood and J. Pitman, Fluctuation identities for Lévy processes and splitting at the maximum;, Adv. Appl. Probab. 12 (1980) 893-902.
    • (1980) Adv. Appl. Probab , vol.12 , pp. 893-902
    • Greenwood, P.1    Pitman, J.2
  • 16
    • 0000968856 scopus 로고
    • On skew Brownian motion
    • J. M. Harrison and L. A. Shepp, On skew Brownian motion;, Ann. Probab. 9 (1981) 309-313.
    • (1981) Ann. Probab , vol.9 , pp. 309-313
    • Harrison, J.M.1    Shepp, L.A.2
  • 17
    • 0023069772 scopus 로고
    • The sampling theory of neutral alleles and an urn model in population genetics
    • F. M. Hoppe, The sampling theory of neutral alleles and an urn model in population genetics;, J. Math. Biol. 25 (1987) 123-159.
    • (1987) J. Math. Biol , vol.25 , pp. 123-159
    • Hoppe, F.M.1
  • 19
    • 0007373304 scopus 로고
    • Canonical representations and convergence criteria for processes with exchangeable increments
    • O. Kallenberg, Canonical representations and convergence criteria for processes with exchangeable increments;, Z. Wahrsch. verw. Gebiete 27 (1973) 23-36.
    • (1973) Z. Wahrsch. Verw. Gebiete , vol.27 , pp. 23-36
    • Kallenberg, O.1
  • 20
    • 0004212801 scopus 로고
    • 3rd edn (Akademie Verlag, Berlin, and Academic Press, London)
    • O. Kallenberg, Random measures, 3rd edn (Akademie Verlag, Berlin, and Academic Press, London, 1983).
    • (1983) Random measures
    • Kallenberg, O.1
  • 21
    • 0038659612 scopus 로고
    • Splitting at backward times in regenerative sets
    • O. Kallenberg, Splitting at backward times in regenerative sets;, Ann. Probab. 9 (1981) 781-799.
    • (1981) Ann. Probab , vol.9 , pp. 781-799
    • Kallenberg, O.1
  • 23
  • 24
    • 0042784843 scopus 로고
    • Oscillating Brownian motion
    • J. Keilson and J. A. Wellner, Oscillating Brownian motion;, J. Appl. Probab. 15 (1978) 300-310.
    • (1978) J. Appl. Probab , vol.15 , pp. 300-310
    • Keilson, J.1    Wellner, J.A.2
  • 25
    • 0002453994 scopus 로고
    • Random discrete distributions
    • J. F. C. Kingman, Random discrete distributions;, J. Roy. Statist. Soc. 37 (1975) 1-22.
    • (1975) J. Roy. Statist. Soc , vol.37 , pp. 1-22
    • Kingman, J.F.C.1
  • 26
    • 0039023133 scopus 로고
    • On the duration of the longest excursion
    • (eds E. Cinlar, K. L. Chung, and R. K. Getoor, Birkhäuser, Basel)
    • F. B. Knight, On the duration of the longest excursion;, Seminar on stochastic processes, 1985 (eds E. Cinlar, K. L. Chung, and R. K. Getoor, Birkhäuser, Basel, 1985), pp. 117-148.
    • (1985) Seminar on stochastic processes, 1985 , pp. 117-148
    • Knight, F.B.1
  • 27
    • 84968497856 scopus 로고
    • An occupation time theorem for a class of stochastic processes
    • J. Lamperti, An occupation time theorem for a class of stochastic processes;, Trans. Amer. Math. Soc. 88 (1958) 380-387.
    • (1958) Trans. Amer. Math. Soc , vol.88 , pp. 380-387
    • Lamperti, J.1
  • 28
    • 0039176563 scopus 로고
    • One-dimensional stochastic differential equations involving the local times of the unknown process
    • (eds A. Truman and D. Williams), Lecture Notes in Mathematics 1095 (Springer, Berlin)
    • J. F. Le Gall, One-dimensional stochastic differential equations involving the local times of the unknown process;, Stochastic analysis and applications (eds A. Truman and D. Williams), Lecture Notes in Mathematics 1095 (Springer, Berlin, 1984), pp. 51-82.
    • (1984) Stochastic analysis and applications , pp. 51-82
    • Le Gall, J.F.1
  • 29
    • 0000071308 scopus 로고
    • Sur certains processus stochastiques homogènes
    • P. Lévy, Sur certains processus stochastiques homogènes;, Compositio Math. 7 (1939) 283-339.
    • (1939) Compositio Math , vol.7 , pp. 283-339
    • Lévy, P.1
  • 31
    • 0000944515 scopus 로고
    • Symmetric stable processes as traces of degenerate diffusion processes
    • S. A. Molchanov and E. Ostrovski, Symmetric stable processes as traces of degenerate diffusion processes;, Theor. Prob. Appl. 14, No. 1 (1969) 128-131.
    • (1969) Theor. Prob. Appl , vol.14 , Issue.1 , pp. 128-131
    • Molchanov, S.A.1    Ostrovski, E.2
  • 32
    • 0001451142 scopus 로고
    • Diversity as a concept and its implications for random communities
    • G. P. Patil and C. Taillie, Diversity as a concept and its implications for random communities;, Proc. 41st. I. S. I. New Delhi, 1977, pp. 497-515.
    • (1977) Proc. 41st. I. S. I. New Delhi , pp. 497-515
    • Patil, G.P.1    Taillie, C.2
  • 33
    • 0009234368 scopus 로고
    • Local time is a semi-martingale
    • E. Perkins, Local time is a semi-martingale;, Z. Wahrschein. verw. Gebiete 60 (1982) 79-117.
    • (1982) Z. Wahrschein. Verw. Gebiete , vol.60 , pp. 79-117
    • Perkins, E.1
  • 35
    • 0001902647 scopus 로고
    • Size-biased sampling of Poisson point processes and excursions
    • to appear
    • M. Perman, J. Pitman, and M. Yor, Size-biased sampling of Poisson point processes and excursions;, Probab. Th. Rel. Fields (1992) to appear.
    • (1992) Probab. Th. Rel. Fields
    • Perman, M.1    Pitman, J.2    Yor, M.3
  • 36
    • 0000030777 scopus 로고
    • Asymptotic laws of planar Brownian motion
    • J. Pitman and M. Yor, Asymptotic laws of planar Brownian motion;, Ann. Probab. 14 (1986) 733-779.
    • (1986) Ann. Probab , vol.14 , pp. 733-779
    • Pitman, J.1    Yor, M.2
  • 38
    • 0010265665 scopus 로고
    • Williams; characterisation of the Brownian excursion law: Proof and applications
    • Lecture Notes in Mathematics 850 (Springer, Berlin)
    • L. C. G. Rogers, Williams; characterisation of the Brownian excursion law: Proof and applications;, Séminaire de Probabilités XV, Lecture Notes in Mathematics 850 (Springer, Berlin, 1981), pp. 227-250.
    • (1981) Séminaire de Probabilités XV , pp. 227-250
    • Rogers, L.C.G.1
  • 39
    • 84963036859 scopus 로고
    • A guided tour through excursions
    • L. C. G. Rogers, A guided tour through excursions;, Bull. London Math. Soc. 21 (1989) 305-341.
    • (1989) Bull. London Math. Soc , vol.21 , pp. 305-341
    • Rogers, L.C.G.1
  • 41
    • 0016435271 scopus 로고
    • Limit theorems for solutions to a class of stochastic differential equations
    • W. Rosenkrantz, Limit theorems for solutions to a class of stochastic differential equations;, Indiana Math. J. 24 (1975) 613-625.
    • (1975) Indiana Math. J , vol.24 , pp. 613-625
    • Rosenkrantz, W.1
  • 42
    • 84968490734 scopus 로고
    • Ordered cycle lengths in a random permutation
    • L. A. Shepp and S. P. Lloyd, Ordered cycle lengths in a random permutation;, Trans. Amer. Math Soc. 121 (1966) 340-357.
    • (1966) Trans. Amer. Math Soc , vol.121 , pp. 340-357
    • Shepp, L.A.1    Lloyd, S.P.2
  • 43
    • 0002584967 scopus 로고
    • Limit measures arising in the asymptotic theory of symmetric groups I
    • A. M. Vershik and A. A. Schmidt, Limit measures arising in the asymptotic theory of symmetric groups I;, Theory Probab. Appl. 22, No. 1 (1977) 70-85.
    • (1977) Theory Probab. Appl , vol.22 , Issue.1 , pp. 70-85
    • Vershik, A.M.1    Schmidt, A.A.2
  • 44
    • 0013221038 scopus 로고
    • Limit measures arising in the asymptotic theory of symmetric groups II
    • A. M. Vershik and A. A. Schmidt, Limit measures arising in the asymptotic theory of symmetric groups II;, Theory Probab. Appl. 23, No. 1 (1978) 36-49.
    • (1978) Theory Probab. Appl , vol.23 , Issue.1 , pp. 36-49
    • Vershik, A.M.1    Schmidt, A.A.2
  • 45
    • 0000075616 scopus 로고
    • Astérisque 52-53 (Société Mathématique de France, Paris)
    • J. B. Walsh, A diffusion with discontinuous local time;, Astérisque 52-53 (Société Mathématique de France, Paris, 1978), pp. 37-45.
    • (1978) A diffusion with discontinuous local time , pp. 37-45
    • Walsh, J.B.1
  • 46
    • 0001276580 scopus 로고
    • The stationary distribution of the infinitely many neutral alleles diffusion model
    • G. A. Watterson, The stationary distribution of the infinitely many neutral alleles diffusion model;, J. Appl. Probab. 13 (1976) 639-651.
    • (1976) J. Appl. Probab , vol.13 , pp. 639-651
    • Watterson, G.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.