메뉴 건너뛰기




Volumn 7, Issue 1, 2010, Pages 1-52

Moments of gamma type and the brownian supremum process area

(1)  Janson, Svante a  

a NONE

Author keywords

Brownian motion; Gamma function; Generalized p lya urns.; Moments; Supremum process

Indexed keywords


EID: 84879610987     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/10-PS160     Document Type: Article
Times cited : (46)

References (32)
  • 1
    • 0003851731 scopus 로고
    • Handbook of Mathematical Functions
    • Dover, New York
    • M. Abramowitz & I. A. Stegun, eds., Handbook of Mathematical Functions. Dover, New York, 1972.
    • (1972)
    • Abramowitz, M.1    Stegun, I.A.2
  • 2
    • 0010868667 scopus 로고
    • The cube of a normal distribution is indeterminate
    • MR0929086
    • C. Berg, The cube of a normal distribution is indeterminate. Ann. Probab. 16 (1988), no. 2, 910-913. MR0929086
    • (1988) Ann. Probab , vol.16 , Issue.2 , pp. 910-913
    • Berg, C.1
  • 3
    • 0003571205 scopus 로고
    • Regular Variation
    • Cambridge Univ. Press, Cambridge, MR0898871
    • N. H. Bingham, C. M. Goldie & J. L. Teugels, Regular Variation. Cambridge Univ. Press, Cambridge, 1987. MR0898871
    • (1987)
    • Bingham, N.H.1    Goldie, C.M.2    Teugels, J.L.3
  • 4
    • 0001489723 scopus 로고    scopus 로고
    • Lévy dusts,Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension
    • (3), part A, MR1459089
    • R. Blumenfeld & B. B. Mandelbrot, Lévy dusts,Mittag-Leffler statistics, mass fractal lacunarity, and perceived dimension. Phys. Rev. E (3) 56 (1997), no. 1, part A, 112-118. MR1459089
    • (1997) Phys. Rev. E , vol.56 , Issue.1 , pp. 112-118
    • Blumenfeld, R.1    Mandelbrot, B.B.2
  • 5
    • 0003318954 scopus 로고
    • Generalized gamma convolutions and related classes of distributions and densities
    • Springer-Verlag, New York, MR1224674
    • L. Bondesson, Generalized gamma convolutions and related classes of distributions and densities. Lecture Notes in Statistics 76, Springer-Verlag, New York, 1992. MR1224674
    • (1992) Lecture Notes in Statistics , vol.76
    • Bondesson, L.1
  • 6
    • 84890702668 scopus 로고
    • Handbuch der Laplace-transformation I
    • MR0344808
    • G. Doetsch, Handbuch der Laplace-transformation I, Birkḧauser, Basel, 1950. MR0344808
    • (1950) Birkḧauser, Basel
    • Doetsch, G.1
  • 8
    • 84968508674 scopus 로고
    • Fluctuation theory of recurrent events
    • MR0032114
    • W. Feller, Fluctuation theory of recurrent events. Trans. Amer. Math. Soc. 67 (1949), 98-119. MR0032114
    • (1949) Trans. Amer. Math. Soc , vol.67 , pp. 98-119
    • Feller, W.1
  • 9
    • 0003421261 scopus 로고
    • An Introduction to Probability Theory and its Applications
    • 2nd ed., Wiley, New York, MR0270403
    • W. Feller, An Introduction to Probability Theory and its Applications, Volume II, 2nd ed., Wiley, New York, 1971. MR0270403
    • (1971) , vol.2
    • Feller, W.1
  • 10
    • 61449105046 scopus 로고    scopus 로고
    • Some exactly solvable models of urn process theory
    • Proc. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities,MR2509623
    • P. Flajolet, P. Dumas & V. Puyhaubert, Some exactly solvable models of urn process theory. Proc. Fourth Colloquium on Mathematics and Computer Science Algorithms, Trees, Combinatorics and Probabilities, Discrete Math. Theor. Comput. Sci. Proc. AG, 2006, 59-118. MR2509623
    • (2006) Discrete Math. Theor. Comput. Sci. Proc. AG , pp. 59-118
    • Flajolet, P.1    Dumas, P.2    Puyhaubert, V.3
  • 11
    • 0029326388 scopus 로고
    • Mellin transforms and asymptotics: harmonic sums
    • MR1337752
    • P. Flajolet, X. Gourdon & P. Dumas, Mellin transforms and asymptotics: harmonic sums. Theor. Computer Science 144 (1995), 3-58. MR1337752
    • (1995) Theor. Computer Science , vol.144 , pp. 3-58
    • Flajolet, P.1    Gourdon, X.2    Dumas, P.3
  • 15
    • 1542288384 scopus 로고    scopus 로고
    • Functional limit theorems for multitype branching processes and generalized P'olya urns
    • MR2040966
    • S. Janson, Functional limit theorems for multitype branching processes and generalized P'olya urns. Stochastic Process. Appl. 110 (2004), no. 2, 177-245. MR2040966
    • (2004) Stochastic Process. Appl , vol.110 , Issue.2 , pp. 177-245
    • Janson, S.1
  • 16
    • 36049016729 scopus 로고    scopus 로고
    • Limit theorems for triangular urn schemes
    • MR2226887
    • S. Janson, Limit theorems for triangular urn schemes. Probab. Theory Rel. Fields 134 (2005), 417-452. MR2226887
    • (2005) Probab. Theory Rel. Fields , vol.134 , pp. 417-452
    • Janson, S.1
  • 17
    • 34548246341 scopus 로고    scopus 로고
    • Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas
    • MR2318402
    • S. Janson, Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas. Probability Surveys 4 (2007), 80-145. MR2318402
    • (2007) Probability Surveys , vol.4 , pp. 80-145
    • Janson, S.1
  • 18
    • 38149029082 scopus 로고    scopus 로고
    • Tail estimates for the Brownian excursion area and other Brownian areas
    • MR2365879
    • S. Janson & G. Louchard, Tail estimates for the Brownian excursion area and other Brownian areas. Electronic J. Probab. 12 (2007), no. 58, 1600-1632. MR2365879
    • (2007) Electronic J. Probab , vol.12 , Issue.58 , pp. 1600-1632
    • Janson, S.1    Louchard, G.2
  • 19
    • 67949089773 scopus 로고    scopus 로고
    • The integral of the supremum process of Brownian motion
    • MR2535835
    • S. Janson & N. Petersson, The integral of the supremum process of Brownian motion. J. Appl. Probab. 46 (2009), no. 2, 593-600. MR2535835
    • (2009) J. Appl. Probab , vol.46 , Issue.2 , pp. 593-600
    • Janson, S.1    Petersson, N.2
  • 21
    • 0003910552 scopus 로고
    • Extremes and Related Properties of Random Sequences and Processes
    • Springer-Verlag, New York, MR0691492
    • M. R. Leadbetter, G. Lindgren & H. Rootzén, Extremes and Related Properties of Random Sequences and Processes. Springer-Verlag, New York, 1983. MR0691492
    • (1983)
    • Leadbetter, M.R.1    Lindgren, G.2    Rootzén, H.3
  • 22
    • 33746386118 scopus 로고
    • Sur les fonctions indépendants III
    • J. Marcinkiewicz, Sur les fonctions indépendants III. Fund. Math. 31 (1938), 86-102.
    • (1938) Fund. Math , vol.31 , pp. 86-102
    • Marcinkiewicz, J.1
  • 23
    • 19044384354 scopus 로고
    • Sur la représentation analytique d'une branche uniforme d'une fonction monogène (cinquième note)
    • MR1555012
    • G. Mittag-Leffler, Sur la représentation analytique d'une branche uniforme d'une fonction monogène (cinquième note). Acta Math. 29 (1905), no. 1, 101-181. MR1555012
    • (1905) Acta Math , vol.29 , Issue.1 , pp. 101-181
    • Mittag-Leffler, G.1
  • 24
    • 84890729108 scopus 로고    scopus 로고
    • The maximum displacement for linear probing hashing I
    • Uppsala. In The Maximum Displacement for Linear Probing Hashing, Ph. D. thesis, Uppsala
    • N. Petersson, The maximum displacement for linear probing hashing I. Tech. report 2008:8, Uppsala. In The Maximum Displacement for Linear Probing Hashing, Ph. D. thesis, Uppsala, 2009.
    • (2009) Tech. report 2008 , vol.8
    • Petersson, N.1
  • 25
    • 0000495328 scopus 로고
    • On Mittag-Leffler functions and related distributions
    • MR1054728
    • R. N. Pillai, On Mittag-Leffler functions and related distributions. Ann. Inst. Statist. Math. 42 (1990), no. 1, 157-161. MR1054728
    • (1990) Ann. Inst. Statist. Math , vol.42 , Issue.1 , pp. 157-161
    • Pillai, R.N.1
  • 27
    • 0001453215 scopus 로고
    • Sur quelques points de la théorie des probabilités
    • G. Pólya, Sur quelques points de la théorie des probabilités. Ann. Inst. Poincaré 1 (1931), 117-161.
    • (1931) Ann. Inst. Poincaré , vol.1 , pp. 117-161
    • Pólya, G.1
  • 31
    • 0000848317 scopus 로고
    • The moment problem for polynomial forms in normal random variables
    • MR1245307
    • E. V. Slud, The moment problem for polynomial forms in normal random variables. Ann. Probab. 21 (1993), no. 4, 2200-2214. MR1245307
    • (1993) Ann. Probab , vol.21 , Issue.4 , pp. 2200-2214
    • Slud, E.V.1
  • 32
    • 0002593008 scopus 로고
    • Recherches sur les fractions continues
    • 9(A) (1895), 1-47. Reprinted in Oeuvres Complètes 2, pp. 402-566, Noordhoff, Groningen, 1918. MR1344720
    • T. J. Stieltjes, Recherches sur les fractions continues. Ann. Fac. Sci. Toulouse Math. 8(J) (1894), 1-122; 9(A) (1895), 1-47. Reprinted in Oeuvres Complètes 2, pp. 402-566, Noordhoff, Groningen, 1918. MR1344720
    • (1894) Ann. Fac. Sci. Toulouse Math , vol.8 , Issue.J , pp. 1-122
    • Stieltjes, T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.