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Volumn 6, Issue 4, 1996, Pages 1091-1111

On the distribution of Brownian areas

Author keywords

Absolute value; Airy functions; Area; Asymptotic distribution; Brownian bridge; Brownian excursion; Brownian motion; Feynman Kac; Inversion; Moments; Positive part; Recursion formulas

Indexed keywords


EID: 0030365084     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1035463325     Document Type: Article
Times cited : (50)

References (36)
  • 3
    • 0002859752 scopus 로고
    • Valuers principales associées aux temps locaux Browniens
    • BIANE, PH. and YOR, M. (1987). Valuers principales associées aux temps locaux Browniens. Bull. Sci. Math. 111 23-101.
    • (1987) Bull. Sci. Math. , vol.111 , pp. 23-101
    • Biane, Ph.1    Yor, M.2
  • 4
    • 0000268170 scopus 로고
    • Sur la loi des temps locaux browniens pris en un temps exponentiel
    • Springer, New York
    • BIANE, PH. and YOR, M. (1988). Sur la loi des temps locaux browniens pris en un temps exponentiel. Séminaire de Probabilités XXII. Lecture Notes in Math. 1321 454-465. Springer, New York.
    • (1988) Séminaire de Probabilités XXII. Lecture Notes in Math. , vol.1321 , pp. 454-465
    • Biane, Ph.1    Yor, M.2
  • 5
    • 0041713725 scopus 로고
    • Two simple distribution-free tests of goodness of fit
    • BIRNBAUM, Z. W. and TANG, V. K. T. (1964). Two simple distribution-free tests of goodness of fit. Rev. Internat. Statist. Inst. 32 2-13.
    • (1964) Rev. Internat. Statist. Inst. , vol.32 , pp. 2-13
    • Birnbaum, Z.W.1    Tang, V.K.T.2
  • 6
    • 0039034658 scopus 로고
    • Distribution of integral functionals of a Brownian motion
    • BORODIN, A. N. (1984). Distribution of integral functionals of a Brownian motion. J. Soviet Math. 27 3005-3022.
    • (1984) J. Soviet Math. , vol.27 , pp. 3005-3022
    • Borodin, A.N.1
  • 7
    • 0043216420 scopus 로고
    • A comparative study of several one-sided goodness-of-fit tests
    • CHAPMAN, D. G. (1958). A comparative study of several one-sided goodness-of-fit tests. Ann. Math. Statist. 29 655.
    • (1958) Ann. Math. Statist. , vol.29 , pp. 655
    • Chapman, D.G.1
  • 8
    • 0001023059 scopus 로고
    • Contributi intorno ad un test per l'omogeneità tra du campioni
    • CIFARELLI, D. M. (1975). Contributi intorno ad un test per l'omogeneità tra du campioni. G. Econom. Ann. Econ. (N.S.) 34 233-249.
    • (1975) G. Econom. Ann. Econ. (N.S.) , vol.34 , pp. 233-249
    • Cifarelli, D.M.1
  • 9
    • 0038931965 scopus 로고
    • On the supremum of a certain Gaussian process
    • DARLING, D. A. (1983). On the supremum of a certain Gaussian process. Ann. Probab. 11 803-806.
    • (1983) Ann. Probab. , vol.11 , pp. 803-806
    • Darling, D.A.1
  • 10
    • 0001644066 scopus 로고
    • Functionals of Brownian meander and excursion
    • DURRETT, R. T. and IGLEHART, D. L. (1977). Functionals of Brownian meander and excursion. Ann. Probab. 5 130-135.
    • (1977) Ann. Probab. , vol.5 , pp. 130-135
    • Durrett, R.T.1    Iglehart, D.L.2
  • 13
    • 0007197086 scopus 로고
    • Excursions of a Markov process
    • GETOOR, R. K. (1979). Excursions of a Markov process. Ann. Probab. 7 244-266.
    • (1979) Ann. Probab. , vol.7 , pp. 244-266
    • Getoor, R.K.1
  • 15
    • 0002641355 scopus 로고
    • Brownian motion with a parabolic drift and Airy functions
    • GROENEBOOM, P. (1989). Brownian motion with a parabolic drift and Airy functions. Probab. Theory Related Fields 81 79-109.
    • (1989) Probab. Theory Related Fields , vol.81 , pp. 79-109
    • Groeneboom, P.1
  • 18
    • 84966226212 scopus 로고
    • On the average of a certain Wiener functional and a related limit theorem in calculus of probability
    • KAC, M. (1946). On the average of a certain Wiener functional and a related limit theorem in calculus of probability. Trans. Amer. Math. Soc. 59 401-414.
    • (1946) Trans. Amer. Math. Soc. , vol.59 , pp. 401-414
    • Kac, M.1
  • 19
    • 0003021436 scopus 로고
    • On some connections between probability theory and differential and integral equations
    • Univ. California Press, Berkeley
    • KAC, M. (1951). On some connections between probability theory and differential and integral equations. Proc. Second Berkeley Symp. Math. Statist. Probab. 1 189-215. Univ. California Press, Berkeley.
    • (1951) Proc. Second Berkeley Symp. Math. Statist. Probab. , vol.1 , pp. 189-215
    • Kac, M.1
  • 21
    • 0021493799 scopus 로고
    • Kac's formula, Lévy's local time and Brownian excursion
    • LOUCHARD, G. (1984a). Kac's formula, Lévy's local time and Brownian excursion. J. Appl. Probab. 21 479-499.
    • (1984) J. Appl. Probab. , vol.21 , pp. 479-499
    • Louchard, G.1
  • 22
    • 0021625402 scopus 로고
    • The Brownian excursion area
    • Erratum: A12 (1986) 375
    • LOUCHARD, G. (1984b). The Brownian excursion area. Comput. Math. Appl. 10 413-417. Erratum: A12 (1986) 375.
    • (1984) Comput. Math. Appl. , vol.10 , pp. 413-417
    • Louchard, G.1
  • 23
    • 0042715252 scopus 로고
    • Ueber die entwicklung einer beliebigen funktion nach laguerreschen polynomen
    • NASAROW, N. (1931). Ueber die Entwicklung einer beliebigen Funktion nach Laguerreschen Polynomen. Math. Z. 33 481-487.
    • (1931) Math. Z. , vol.33 , pp. 481-487
    • Nasarow, N.1
  • 25
    • 0000637519 scopus 로고
    • The integral of the absolute value of the pinned Wiener process
    • RICE, S. O. (1982). The integral of the absolute value of the pinned Wiener process. Ann. Probab. 10 240-243.
    • (1982) Ann. Probab. , vol.10 , pp. 240-243
    • Rice, S.O.1
  • 29
    • 0000637518 scopus 로고
    • On the integral of the absolute value of the pinned Wiener process
    • SHEPP, L. A. (1982). On the integral of the absolute value of the pinned Wiener process. Ann. Probab. 10 234-239. [Acknowledgment of priority. Ann. Probab. (1991) 19 1397.]
    • (1982) Ann. Probab. , vol.10 , pp. 234-239
    • Shepp, L.A.1
  • 30
    • 0347148268 scopus 로고
    • Acknowledgment of priority
    • SHEPP, L. A. (1982). On the integral of the absolute value of the pinned Wiener process. Ann. Probab. 10 234-239. [Acknowledgment of priority. Ann. Probab. (1991) 19 1397.]
    • (1991) Ann. Probab. , vol.19 , pp. 1397
  • 32
    • 0011400157 scopus 로고
    • Random walk processes and their application in order statistics
    • TAKÁCS, L. (1992b). Random walk processes and their application in order statistics. Ann. Appl. Probab. 2 435-459.
    • (1992) Ann. Appl. Probab. , vol.2 , pp. 435-459
    • Takács, L.1
  • 33
    • 0000752136 scopus 로고
    • On the distribution of the integral of the absolute value of the Brownian motion
    • TAKÁCS, L. (1993a). On the distribution of the integral of the absolute value of the Brownian motion. Ann. Appl. Probab. 3 186-197.
    • (1993) Ann. Appl. Probab. , vol.3 , pp. 186-197
    • Takács, L.1
  • 34
    • 4243314432 scopus 로고
    • Personal communication with J. A. Wellner
    • TAKÁCS, L. (1993b). Personal communication with J. A. Wellner.
    • (1993)
    • Takács, L.1
  • 35
    • 0007456381 scopus 로고
    • On the development of arbitrary functions in series of Hermite's and Laguerre's polynomials
    • USPENSKY, J. V. (1927). On the development of arbitrary functions in series of Hermite's and Laguerre's polynomials. Ann. Math. 28 593-619.
    • (1927) Ann. Math. , vol.28 , pp. 593-619
    • Uspensky, J.V.1


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