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References

  1. Bleistein, Norman; Handelsman, Richard A. Asymptotic expansions of integrals. Second edition. Dover Publications, Inc., New York, 1986. xvi+425 pp. ISBN: 0-486-65082-0 MR0863284 (89d:41049)
  2. Csörgö, Miklós; Shi, Zhan; Yor, Marc. Some asymptotic properties of the local time of the uniform empirical process. Bernoulli 5 (1999), no. 6, 1035--1058. MR1735784 (2001a:60090)
  3. Darling, D. A. On the supremum of a certain Gaussian process. Ann. Probab. 11 (1983), no. 3, 803--806. MR0704564 (84f:60058)
  4. Davies, Laurie. Tail probabilities for positive random variables with entire characteristic functions of very regular growth. Vorträge der Wissenschaftlichen Jahrestagung der Gesellschaft für Angewandte Mathematik und Mechanik (Göttingen, 1975). Z. Angew. Math. Mech. 56 (1976), no. 3, T334--T336. MR0431331 (55 #4332)
  5. Fatalov, V. R. Asymptotics of large deviations of Gaussian processes of Wiener type for $Lsp p$-functionals, $p>0$, and the hypergeometric function. (Russian) Mat. Sb. 194 (2003), no. 3, 61--82; translation in Sb. Math. 194 (2003), no. 3-4, 369--390 MR1992557 (2004d:60010)
  6. Flajolet, P.; Louchard, G. Analytic variations on the Airy distribution. Mathematical analysis of algorithms. Algorithmica 31 (2001), no. 3, 361--377. MR1855255 (2002j:68115)
  7. Janson, Svante; Chassaing, Philippe. The center of mass of the ISE and the Wiener index of trees. Electron. Comm. Probab. 9 (2004), 178--187 (electronic). MR2108865 (2005k:60303)
  8. Janson, Svante. Brownian excursion area, Wright's constants in graph enumeration, and other Brownian areas. Probab. Surv. 4 (2007), 80--145 (electronic). MR2318402
  9. Kac, M. On the average of a certain Wiener functional and a related limit theorem in calculus of probability. Trans. Amer. Math. Soc. 59, (1946). 401--414. MR0016570 (8,37b)
  10. Kasahara, Yuji. Tauberian theorems of exponential type. J. Math. Kyoto Univ. 18 (1978), no. 2, 209--219. MR0501841 (80g:40008)
  11. Louchard, G. Kac's formula, Levy's local time and Brownian excursion. J. Appl. Probab. 21 (1984), no. 3, 479--499. MR0752014 (86f:60100)
  12. Louchard, G. The Brownian excursion area: a numerical analysis. Comput. Math. Appl. 10 (1984), no. 6, 413--417 (1985). MR0783514 (87b:60123a)
  13. Majumdar, Satya N.; Comtet, Alain. Airy distribution function: from the area under a Brownian excursion to the maximal height of fluctuating interfaces. J. Stat. Phys. 119 (2005), no. 3-4, 777--826. MR2151223 (2006a:82057)
  14. Milnor, J. Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51 Princeton University Press, Princeton, N.J. 1963 vi+153 pp. MR0163331 (29 #634)
  15. Perman, Mihael; Wellner, Jon A. On the distribution of Brownian areas. Ann. Appl. Probab. 6 (1996), no. 4, 1091--1111. MR1422979 (97m:60119)
  16. Revuz, Daniel; Yor, Marc. Continuous martingales and Brownian motion. Third edition. Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 293. Springer-Verlag, Berlin, 1999. xiv+602 pp. ISBN: 3-540-64325-7 MR1725357 (2000h:60050)
  17. Shepp, L. A. On the integral of the absolute value of the pinned Wiener process. Ann. Probab. 10 (1982), no. 1, 234--239. MR0637389 (82m:60100)
  18. Takács, Lajos. A Bernoulli excursion and its various applications. Adv. in Appl. Probab. 23 (1991), no. 3, 557--585. MR1122875 (92m:60057)
  19. Takács, Lajos. Random walk processes and their applications in order statistics. Ann. Appl. Probab. 2 (1992), no. 2, 435--459. MR1161061 (93h:60114)
  20. Takács, Lajos. On the distribution of the integral of the absolute value of the Brownian motion. Ann. Appl. Probab. 3 (1993), no. 1, 186--197. MR1202522 (93i:60154)
  21. Takács, Lajos. Limit distributions for the Bernoulli meander. J. Appl. Probab. 32 (1995), no. 2, 375--395. MR1334893 (96c:60087)
  22. Tolmatz, Leonid. Asymptotics of the distribution of the integral of the absolute value of the Brownian bridge for large arguments. Ann. Probab. 28 (2000), no. 1, 132--139. MR1756000 (2002a:60068)
  23. Tolmatz, Leonid. The saddle point method for the integral of the absolute value of the Brownian motion. Discrete random walks (Paris, 2003), 309--324 (electronic), Discrete Math. Theor. Comput. Sci. Proc., AC, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2003. MR2042397 (2004m:60178)
  24. Tolmatz, Leonid. Asymptotics of the distribution of the integral of the positive part of the Brownian bridge for large arguments. J. Math. Anal. Appl. 304 (2005), no. 2, 668--682. MR2126559 (2006b:60179)
  25. Vervaat, Wim. A relation between Brownian bridge and Brownian excursion. Ann. Probab. 7 (1979), no. 1, 143--149. MR0515820 (80b:60107)


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