메뉴 건너뛰기




Volumn 47, Issue 4, 2011, Pages 1096-1120

Exponential functionals of Brownian motion and class-one Whittaker functions

Author keywords

Conditioned Brownian motion; Quantum Toda lattice

Indexed keywords


EID: 80054106617     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1214/10-AIHP401     Document Type: Article
Times cited : (32)

References (29)
  • 1
    • 0012905502 scopus 로고    scopus 로고
    • On a triplet of exponential Brownian functionals
    • Séminaire de probabilités de Strasbourg XXXV Springer, Berlin. MR1837300
    • L. Alili, H. Matsumoto and T. Shiraishi. On a triplet of exponential Brownian functionals. In Séminaire de probabilités de Strasbourg, XXXV 396-415. Lecture Notes in Math. 1755. Springer, Berlin, 2001. MR1837300
    • (2001) Lecture Notes in Math. , vol.1755 , pp. 396-415
    • Alili, L.1    Matsumoto, H.2    Shiraishi, T.3
  • 2
    • 0002325272 scopus 로고    scopus 로고
    • Further exponential generalization of Pitman's 2M-X theorem
    • F. Baudoin. Further exponential generalization of Pitman's 2M ? X theorem. Electron. Comm. Probab. 7 (2002) 37-46 (electronic). MR1887172 (Pubitemid 38817998)
    • (2002) Electronic Communications in Probability , vol.7 , pp. 37-46
    • Baudoin, F.1
  • 3
    • 0036062859 scopus 로고    scopus 로고
    • Conditioned stochastic differential equations: Theory, examples and applications to finance
    • MR1919610
    • F. Baudoin. Conditioned stochastic differential equations: Theory, examples and applications to finance. Stochastic Process. Appl. 100 (2002) 109-145. MR1919610
    • (2002) Stochastic Process. Appl. , vol.100 , pp. 109-145
    • Baudoin, F.1
  • 4
    • 28444455259 scopus 로고    scopus 로고
    • Littelmann paths and brownian paths
    • DOI 10.1215/S0012-7094-05-13014-9
    • P. Biane, P. Bougerol and N. O'Connell. Littelmann paths and Brownian paths. Duke Math. J. 130 (2005) 127-167. MR2176549 (Pubitemid 41730578)
    • (2005) Duke Mathematical Journal , vol.130 , Issue.1 , pp. 127-167
    • Biane, P.1    Bougerol, P.2    O'Connell, N.3
  • 5
    • 0036882777 scopus 로고    scopus 로고
    • Paths in Weyl chambers and random matrices
    • MR1942321
    • P. Bougerol and T. Jeulin. Paths in Weyl chambers and random matrices. Probab. Theory Related Fields 124 (2002) 517-543. MR1942321
    • (2002) Probab. Theory Related Fields , vol.124 , pp. 517-543
    • Bougerol, P.1    Jeulin, T.2
  • 6
    • 0742268058 scopus 로고
    • Automorphic forms on GL(3,R )
    • Springer, Berlin. MR0765698
    • D. Bump. Automorphic Forms on GL(3,R). Lecture Notes in Math. 1083. Springer, Berlin, 1984. MR0765698
    • (1984) Lecture Notes in Math. , vol.1083
    • Bump, D.1
  • 7
    • 51249163948 scopus 로고
    • Unramified Whittaker functions for GL(3,R)
    • MR1335367
    • D. Bump and J. Huntley. Unramified Whittaker functions for GL(3,R). J. Anal. Math. 65 (1995) 19-44. MR1335367
    • (1995) J. Anal. Math. , vol.65 , pp. 19-44
    • Bump, D.1    Huntley, J.2
  • 8
    • 0035271334 scopus 로고    scopus 로고
    • The integral of geometric Brownian motion
    • DOI 10.1239/aap/999187905
    • D. Dufresne. The integral of geometric Brownian motion. Adv. in Appl. Probab. 33 (2001) 223-241. MR1825324 (Pubitemid 32443977)
    • (2001) Advances in Applied Probability , vol.33 , Issue.1 , pp. 223-241
    • Dufresne, D.1
  • 9
    • 3042522448 scopus 로고    scopus 로고
    • On distributions associated with the generalized Lévy's stochastic area formula
    • DOI 10.1556/SScMath.41.2004.1.5
    • R. Ghomrasni. On distribution associated with the generalized Levy's stochastic area formula. Studia Sci. Math. Hungar. 41 (2004) 93-100. MR2082064 (Pubitemid 38834992)
    • (2004) Studia Scientiarum Mathematicarum Hungarica , vol.41 , Issue.1 , pp. 93-100
    • Ghomrasni, R.1
  • 10
    • 0001178133 scopus 로고
    • The Plancherel measure for Riemannian symmetric spaces with non-positive curvature
    • MR0150239
    • S. G. Gindikin and F. I. Karpelevich. The Plancherel measure for Riemannian symmetric spaces with non-positive curvature. Dokl. Akad. Nauk USSR 145 (1962) 252-255. MR0150239
    • (1962) Dokl. Akad. Nauk USSR , vol.145 , pp. 252-255
    • Gindikin, S.G.1    Karpelevich, F.I.2
  • 11
    • 0009242617 scopus 로고    scopus 로고
    • Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture
    • Topics in Singularity Theory. AMS, Providence, RI. MR1767115
    • A. Givental. Stationary phase integrals, quantum Toda lattices, flag manifolds and the mirror conjecture. In Topics in Singularity Theory 103-115. AMS Transl. Ser. 2 180. AMS, Providence, RI, 1997. MR1767115
    • (1997) AMS Transl. ser , vol.180 , Issue.2 , pp. 103-115
    • Givental, A.1
  • 12
    • 0039493244 scopus 로고
    • The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential
    • MR0969177
    • C. Grosche. The path integral on the Poincaré upper half-plane with a magnetic field and for the Morse potential. Ann. Phys. 187 (1988) 110-134. MR0969177
    • (1988) Ann. Phys. , vol.187 , pp. 110-134
    • Grosche, C.1
  • 13
    • 84972502525 scopus 로고
    • Whittaker functions on semisimple Lie groups
    • MR0665496
    • M. Hashizume. Whittaker functions on semisimple Lie groups. Hiroshima Math. J. 12 (1982) 259-293. MR0665496
    • (1982) Hiroshima Math. J. , vol.12 , pp. 259-293
    • Hashizume, M.1
  • 14
    • 0003065227 scopus 로고    scopus 로고
    • Brownian motion on the Hyperbolic plane and Selberg trace formula
    • MR1682843
    • N. Ikeda and H. Matsumoto. Brownian motion on the Hyperbolic plane and Selberg trace formula. J. Funct. Anal. 163 (1999) 63-110. MR1682843
    • (1999) J. Funct. Anal. , vol.163 , pp. 63-110
    • Ikeda, N.1    Matsumoto, H.2
  • 15
    • 0001416265 scopus 로고
    • Fonctions de Whittaker associées aux groupes de Chevalley
    • MR0271275
    • H. Jacquet. Fonctions de Whittaker associées aux groupes de Chevalley. Bull. Soc. Math. France 95 (1967) 243-309. MR0271275
    • (1967) Bull. Soc. Math. France , vol.95 , pp. 243-309
    • Jacquet, H.1
  • 16
    • 0010230966 scopus 로고    scopus 로고
    • Integral representations for the eigenfunctions of a quantum periodic Toda chain
    • MR1751619
    • S. Kharchev and D. Lebedev. Integral representations for the eigenfunctions of a quantum periodic Toda chain. Lett. Math. Phys. 50 (1999) 53-77. MR1751619
    • (1999) Lett. Math. Phys. , vol.50 , pp. 53-77
    • Kharchev, S.1    Lebedev, D.2
  • 17
    • 0001043985 scopus 로고
    • Quantisation and representation theory
    • Representation Theory of Lie Groups, Proc. SRC/LMS Research Symposium, Oxford 1977. Cambridge Univ. Press, Cambridge. MR0568880
    • B. Kostant. Quantisation and representation theory. In Representation Theory of Lie Groups, Proc. SRC/LMS Research Symposium, Oxford 1977 287-316. LMS Lecture Notes 34. Cambridge Univ. Press, Cambridge, 1977. MR0568880
    • (1977) LMS Lecture Notes , vol.34 , pp. 287-316
    • Kostant, B.1
  • 19
    • 0033147983 scopus 로고    scopus 로고
    • A version of Pitman's 2M ?X theorem for geometric Brownian motions
    • MR1696208
    • H. Matsumoto and M. Yor. A version of Pitman's 2M ?X theorem for geometric Brownian motions. C. R. Acad. Sci. Paris Sér. 1 328 (1999) 1067-1074. MR1696208
    • (1999) C. R. Acad. Sci. Paris sér 1 , vol.328 , pp. 1067-1074
    • Matsumoto, H.1    Yor, M.2
  • 20
    • 33745855661 scopus 로고    scopus 로고
    • Exponential functionals of Brownian motion, I: Probability laws at a fixed time
    • MR2203675
    • H. Matsumoto and M. Yor. Exponential functionals of Brownian motion, I: Probability laws at a fixed time. Probab. Surv. 2 (2005) 312-347. MR2203675
    • (2005) Probab. Surv. , vol.2 , pp. 312-347
    • Matsumoto, H.1    Yor, M.2
  • 21
    • 0001033078 scopus 로고    scopus 로고
    • A relationship between Brownian motions with opposite drifts
    • MR1833628
    • H. Matsumoto and M. Yor. A relationship between Brownian motions with opposite drifts. Osaka J. Math. 38 (2001) 383-398. MR1833628
    • (2001) Osaka J. Math. , vol.38 , pp. 383-398
    • Matsumoto, H.1    Yor, M.2
  • 22
    • 80054116410 scopus 로고    scopus 로고
    • Directed polymers and the quantum Toda lattice
    • To appear, arXiv: 0910.0069
    • N. O'Connell. Directed polymers and the quantum Toda lattice. Ann. Probab. To appear, 2011. Available at arXiv:0910.0069.
    • (2011) Ann. Probab
    • O'connell, N.1
  • 23
    • 0000804956 scopus 로고    scopus 로고
    • Brownian analogues of Burke's theorem
    • DOI 10.1016/S0304-4149(01)00119-3, PII S0304414901001193
    • N. O'Connell and M. Yor. Brownian analogues of Burke's theorem. Stochastic Process. Appl. 96 (2001) 285-304. MR1865759 (Pubitemid 33632186)
    • (2001) Stochastic Processes and their Applications , vol.96 , Issue.2 , pp. 285-304
    • O'Connell, N.1    Yor, M.2
  • 25
    • 0000884985 scopus 로고
    • One-dimensional Brownian motion and the three-dimensional Bessel process
    • MR0375485
    • J. W. Pitman. One-dimensional Brownian motion and the three-dimensional Bessel process. Adv. in Appl. Probab. 7 (1975) 511-526. MR0375485
    • (1975) Adv. in Appl. Probab. , vol.7 , pp. 511-526
    • Pitman, J.W.1
  • 26
    • 0001380232 scopus 로고
    • Markov functions
    • MR0624684
    • L. C. G. Rogers and J. Pitman. Markov functions. Ann. Probab. 9 (1981) 573-582. MR0624684
    • (1981) Ann. Probab. , vol.9 , pp. 573-582
    • Rogers, L.C.G.1    Pitman, J.2
  • 27
    • 0039824313 scopus 로고
    • Quantisation of open toda lattices
    • Dynamical Systems VII: Integrable Systems, Nonholonomic Dynamical Systems V. I. Arnol'd and S. P. Novikov (Eds) Springer, Berlin. MR1256257
    • M. Semenov-Tian-Shansky. Quantisation of open Toda lattices. In Dynamical Systems VII: Integrable Systems, Nonholonomic Dynamical Systems 226-259. V. I. Arnol'd and S. P. Novikov (Eds). Encyclopaedia of Mathematical Sciences 16. Springer, Berlin, 1994. MR1256257
    • (1994) Encyclopaedia of Mathematical Sciences , vol.16 , pp. 226-259
    • Semenov-Tian-Shansky, M.1
  • 28
    • 84972560567 scopus 로고
    • Poincaré series for GL(3,R)-Whittaker functions
    • MR1016442
    • E. Stade. Poincaré series for GL(3,R)-Whittaker functions. Duke Math. J. 58 (1989) 695-729. MR1016442
    • (1989) Duke Math. J. , vol.58 , pp. 695-729
    • Stade, E.1
  • 29
    • 27144494393 scopus 로고
    • Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem
    • A. Vinogradov and L. Takhtadzhyan. Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem. J. Soviet Math. 18 (1982) 293-324.
    • (1982) J. Soviet Math. , vol.18 , pp. 293-324
    • Vinogradov, A.1    Takhtadzhyan, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.