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Volumn 2, Issue 1, 2005, Pages 348-384

Exponential functionals of brownian motion, II: Some related diffusion processes

Author keywords

Brownian motion; Heat kernel; Hyperbolic space; L vy's theorem; Pitman's theorem; Random environment

Indexed keywords


EID: 33745808966     PISSN: None     EISSN: 15495787     Source Type: Journal    
DOI: 10.1214/154957805100000168     Document Type: Article
Times cited : (98)

References (65)
  • 1
    • 0012905502 scopus 로고    scopus 로고
    • On a triplet of exponential Brownian functionals
    • Lecture Notes in Math., Springer-Verlag. MR1837300
    • Alili, L., Matsumoto, H. and Shiraishi, T. (2001). On a triplet of exponential Brownian functionals, in Séminaire de Probabilités XXXV, 396-415, Lecture Notes in Math., 1755, Springer-Verlag. MR1837300
    • (2001) in Séminaire de Probabilités XXXV , vol.1755 , pp. 396-415
    • Alili, L.1    Matsumoto, H.2    Shiraishi, T.3
  • 3
    • 0039923068 scopus 로고    scopus 로고
    • Stable laws arising from hitting distributions of processes on homogeneous trees and the hyperbolic half-plane
    • MR1815256
    • Baldi, P., Casadio Tarabusi, E. and Figà-Talamanca, A. (2001). Stable laws arising from hitting distributions of processes on homogeneous trees and the hyperbolic half-plane, Pacific J. Math., 197, 257-273. MR1815256
    • (2001) Pacific J. Math. , vol.197 , pp. 257-273
    • Baldi, P.1    Casadio Tarabusi, E.2    Figà-Talamanca, A.3
  • 4
    • 0039192975 scopus 로고    scopus 로고
    • Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities
    • MR1900896
    • Baldi, P., Casadio Tarabusi, E., Figà-Talamanca, A. and Yor, M. (2001). Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities, Rev. Mat. Iberoamericana, 17, 587-605. MR1900896
    • (2001) Rev. Mat. Iberoamericana , vol.17 , pp. 587-605
    • Baldi, P.1    Casadio Tarabusi, E.2    Figà-Talamanca, A.3    Yor, M.4
  • 5
    • 7444237397 scopus 로고    scopus 로고
    • A study of the Hartman- Watson distribution motivated by numerical problems related to the pricing of Asian options
    • MR2122799
    • Barrieu, P., Rouault, A. and Yor, M. (2004). A study of the Hartman- Watson distribution motivated by numerical problems related to the pricing of Asian options, J. Appl. Prob., 41, 1049-1058. MR2122799
    • (2004) J. Appl. Prob. , vol.41 , pp. 1049-1058
    • Barrieu, P.1    Rouault, A.2    Yor, M.3
  • 6
    • 0042199546 scopus 로고
    • Intertwining of Markov semi-groups, some examples
    • Springer-Verlag, Berlin. MR1459446
    • Biane, Ph. (1995). Intertwining of Markov semi-groups, some examples, in Sém. Prob., XXIX, Lecture Notes in Math., 1613, 30-36, Springer-Verlag, Berlin. MR1459446
    • (1995) Sém. Prob., XXIX, Lecture Notes in Math. , vol.1613 , pp. 30-36
    • Biane, Ph.1
  • 7
    • 0000065881 scopus 로고
    • Exemples de théorèmes locaux sur les groupes résolubles
    • MR730116
    • Bougerol, Ph. (1983). Exemples de théorèmes locaux sur les groupes résolubles, Ann. Inst. H.Poincaré, 19, 369-391. MR730116
    • (1983) Ann. Inst. H.Poincaré , vol.19 , pp. 369-391
    • Bougerol, Ph.1
  • 8
    • 0001511096 scopus 로고
    • A one-dimensional diffusion process in a Wiener medium
    • MR866343
    • Brox, T. (1986). A one-dimensional diffusion process in a Wiener medium, Ann. Prob., 14, 1206-1218. MR866343
    • (1986) Ann. Prob. , vol.14 , pp. 1206-1218
    • Brox, T.1
  • 9
    • 21144483893 scopus 로고
    • A conditional approach to the anticipating Girsanov transformation
    • MR1213194
    • Buckdahn, R. and Föllmer, H. (1993). A conditional approach to the anticipating Girsanov transformation, Prob. Theory Relat. Fields, 95, 311-330. MR1213194
    • (1993) Prob. Theory Relat. Fields , vol.95 , pp. 311-330
    • Buckdahn, R.1    Föllmer, H.2
  • 10
    • 0041022515 scopus 로고    scopus 로고
    • Beta-Gamma variables and intertwinings of certain Markov processes
    • Carmona, P. Petit, F. and Yor, M. (1998). Beta-Gamma variables and intertwinings of certain Markov processes, Rev. Mat. Iberoamericana, 14, 311-367.
    • (1998) Rev. Mat. Iberoamericana , vol.14 , pp. 311-367
    • Carmona, P.1    Petit, F.2    Yor, M.3
  • 11
    • 0000210690 scopus 로고
    • On the Landau levels on the hyperbolic plane
    • MR870891
    • Comtet, A. (1987). On the Landau levels on the hyperbolic plane, Ann. Phys., 173, 185-209. MR870891
    • (1987) Ann. Phys. , vol.173 , pp. 185-209
    • Comtet, A.1
  • 12
    • 0009955942 scopus 로고
    • Trace formula for Riemannian surfaces with magnetic field
    • Comtet, A., Georgeot, B. and Ouvry, S. (1993). Trace formula for Riemannian surfaces with magnetic field, Phys. Rev. Lett., 71, 3786-3789.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 3786-3789
    • Comtet, A.1    Georgeot, B.2    Ouvry, S.3
  • 13
    • 0032397394 scopus 로고    scopus 로고
    • Exponential functionals of Brownian motion and disordered systems
    • MR1641852
    • Comtet, A., Monthus, C. and Yor, M. (1998). Exponential functionals of Brownian motion and disordered systems, J. Appl. Prob., 35, 255-271. MR1641852
    • (1998) J. Appl. Prob. , vol.35 , pp. 255-271
    • Comtet, A.1    Monthus, C.2    Yor, M.3
  • 15
    • 0001552273 scopus 로고
    • Analysis on root systems
    • MR918384
    • Debiard, A. and Gaveau, B. (1987). Analysis on root systems, Canad. J. Math., 39, 1281-1404. MR918384
    • (1987) Canad. J. Math. , vol.39 , pp. 1281-1404
    • Debiard, A.1    Gaveau, B.2
  • 16
    • 0035606706 scopus 로고    scopus 로고
    • On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options
    • MR1846094
    • Donati-Martin, C., Ghomrasni, R. and Yor, M. (2001). On certain Markov processes attached to exponential functionals of Brownian motion; application to Asian options, Rev. Mat. Iberoam., 17, 179-193. MR1846094
    • (2001) Rev. Mat. Iberoam. , vol.17 , pp. 179-193
    • Donati-Martin, C.1    Ghomrasni, R.2    Yor, M.3
  • 17
    • 0000929223 scopus 로고    scopus 로고
    • Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions
    • MR1855425
    • Donati-Martin, C., Matsumoto, H. and Yor, M. (2002). Some absolute continuity relationships for certain anticipative transformations of geometric Brownian motions, Publ. RIMS Kyoto Univ., 37, 295-326. MR1855425
    • (2002) Publ. RIMS Kyoto Univ. , vol.37 , pp. 295-326
    • Donati-Martin, C.1    Matsumoto, H.2    Yor, M.3
  • 18
    • 84864849879 scopus 로고
    • The distribution of a perpetuity, with application to risk theory and pension funding
    • MR1129194
    • Dufresne, D. (1990). The distribution of a perpetuity, with application to risk theory and pension funding, Scand. Actuarial J., 39-79. MR1129194
    • (1990) Scand. Actuarial J. , pp. 39-79
    • Dufresne, D.1
  • 19
    • 0001167174 scopus 로고    scopus 로고
    • An affne property of the reciprocal Asian option process
    • MR1833627
    • Dufresne, D. (2001). An affne property of the reciprocal Asian option process, Osaka J. Math., 38, 379-381. MR1833627
    • (2001) Osaka J. Math. , vol.38 , pp. 379-381
    • Dufresne, D.1
  • 20
    • 0035271334 scopus 로고    scopus 로고
    • The integral of geometric Brownian motion
    • MR1825324
    • Dufresne, D. (2001). The integral of geometric Brownian motion, Adv. Appl. Prob., 33, 223-241. MR1825324
    • (2001) Adv. Appl. Prob. , vol.33 , pp. 223-241
    • Dufresne, D.1
  • 22
    • 84941432866 scopus 로고
    • Fourier coeffcients of the resolvent for a Fuchsian group
    • MR506038
    • Fay, J. (1977). Fourier coeffcients of the resolvent for a Fuchsian group, J. Reine Angew. Math., 293, 143-203. MR506038
    • (1977) J. Reine Angew. Math. , vol.293 , pp. 143-203
    • Fay, J.1
  • 23
    • 0000285524 scopus 로고
    • Quelques relations entre processus deBessel, options asiatiques et fonctions con uentes hypergéométriques
    • (Eng. transl. is found in [60].) MR1154389
    • Geman, H. and Yor, M. (1992). Quelques relations entre processus deBessel, options asiatiques et fonctions con uentes hypergéométriques, C.R. Acad. Sci., Paris, Série I, 314, 471-474. (Eng. transl. is found in [60].) MR1154389
    • (1992) C.R. Acad. Sci., Paris, Série I , vol.314 , pp. 471-474
    • Geman, H.1    Yor, M.2
  • 24
    • 84986786403 scopus 로고
    • Bessel processes, Asian options, and perpetuities
    • (also found in [60].)
    • Geman, H. and Yor, M. (1993). Bessel processes, Asian options, and perpetuities, Math. Finance, 3, 349-375. (also found in [60].)
    • (1993) Math. Finance , vol.3 , pp. 349-375
    • Geman, H.1    Yor, M.2
  • 26
    • 0039493244 scopus 로고
    • The path integral on the Poincaré upper half plane with a magnetic field and for the Morse potential
    • MR969177
    • Grosche, C. (1988). The path integral on the Poincaré upper half plane with a magnetic field and for the Morse potential, Ann. Phys. (N.Y.), 187, 110-134. MR969177
    • (1988) Ann. Phys. (N.Y.) , vol.187 , pp. 110-134
    • Grosche, C.1
  • 28
    • 0013004775 scopus 로고    scopus 로고
    • Semi-groupe du mouvement Brownien hyperbolique
    • MR1396754
    • Gruet, J.-C. (1996). Semi-groupe du mouvement Brownien hyperbolique, Stochastics Stochastic Rep., 56, 53-61. MR1396754
    • (1996) Stochastics Stochastic Rep. , vol.56 , pp. 53-61
    • Gruet, J.-C.1
  • 30
    • 33646915441 scopus 로고    scopus 로고
    • Rates of convergence of diffusions with drifted Brownian potentials
    • MR1637078
    • Hu, Y., Shi, Z. and Yor, M. (1999). Rates of convergence of diffusions with drifted Brownian potentials, Trans Amer. Math. Soc., 351, 3915-3934. MR1637078
    • (1999) Trans Amer. Math. Soc. , vol.351 , pp. 3915-3934
    • Hu, Y.1    Shi, Z.2    Yor, M.3
  • 31
    • 0003065227 scopus 로고    scopus 로고
    • Brownian motion on the hyperbolic plane and Selberg trace formula
    • MR1682843
    • Ikeda, N. and Matsumoto, H. (1999). Brownian motion on the hyperbolic plane and Selberg trace formula, J. Func. Anal., 162, 63-110. MR1682843
    • (1999) J. Func. Anal. , vol.162 , pp. 63-110
    • Ikeda, N.1    Matsumoto, H.2
  • 33
    • 28044449348 scopus 로고    scopus 로고
    • Methods for evaluating density functions of exponential functionals represented as integrals of geometric Brownian motion
    • Ishiyama, K. (2005). Methods for evaluating density functions of exponential functionals represented as integrals of geometric Brownian motion, Method. Compu. Appl. Prob., 7, 271-283.
    • (2005) Method. Compu. Appl. Prob. , vol.7 , pp. 271-283
    • Ishiyama, K.1
  • 35
    • 0010823278 scopus 로고
    • On the maximum of a diffusion process in a drifted Brownian environment
    • Lecture Notes in Math. 1557, Springer-Verlag, Berlin. MR1308554
    • Kawazu, K. and Tanaka, H. (1991). On the maximum of a diffusion process in a drifted Brownian environment, in Sém. Prob., XXVII, Lecture Notes in Math. 1557, 78-85, Springer-Verlag, Berlin. MR1308554
    • (1991) in Sém. Prob. , vol.27 , pp. 78-85
    • Kawazu, K.1    Tanaka, H.2
  • 36
    • 33344475302 scopus 로고    scopus 로고
    • A diffusion process in a Brownian environment with drift
    • MR1601361
    • Kawazu, K. and Tanaka, H. (1997). A diffusion process in a Brownian environment with drift, J. Math. Soc. Japan, 49, 189-211. MR1601361
    • (1997) J. Math. Soc. Japan , vol.49 , pp. 189-211
    • Kawazu, K.1    Tanaka, H.2
  • 37
    • 0000469941 scopus 로고
    • The nonlinear transformation of Gaussian measures on Banach space and its absolute continuity
    • Kusuoka, S. (1982). The nonlinear transformation of Gaussian measures on Banach space and its absolute continuity, J. Fac. Sci., Univ. Tokyo Sect. IA, 29, 567-597.
    • (1982) J. Fac. Sci., Univ. Tokyo Sect. IA , vol.29 , pp. 567-597
    • Kusuoka, S.1
  • 40
    • 0345878075 scopus 로고    scopus 로고
    • Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one
    • MR1869991
    • Matsumoto, H. (2001). Closed form formulae for the heat kernels and the Green functions for the Laplacians on the symmetric spaces of rank one, Bull. Sci. math., 125, 553-581. MR1869991
    • (2001) Bull. Sci. math. , vol.125 , pp. 553-581
    • Matsumoto, H.1
  • 41
    • 84890749765 scopus 로고    scopus 로고
    • Subordinators related to the exponential functionals of Brownian bridges and explicit formulae for the semigroup of hyperbolic Brownian motions
    • Proc. 12th Winter School at Siegmundsburg(Germany), R.Buckdahn, H-J.Engelbert and M.Yor, eds., Stochastic Monographs, Taylor & Francis. MR1987318
    • Matsumoto, H., Nguyen, L. and Yor, M. (2002). Subordinators related to the exponential functionals of Brownian bridges and explicit formulae for the semigroup of hyperbolic Brownian motions, in Stochastic Processes and Related Topics, 213-235, Proc. 12th Winter School at Siegmundsburg(Germany), R.Buckdahn, H-J.Engelbert and M.Yor, eds., Stochastic Monographs, Vol. 12, Taylor & Francis. MR1987318
    • (2002) in Stochastic Processes and Related Topics , vol.12 , pp. 213-235
    • Matsumoto, H.1    Nguyen, L.2    Yor, M.3
  • 42
    • 3142680822 scopus 로고    scopus 로고
    • Markov or non-Markov property of cM - X processes
    • MR2048472
    • Matsumoto, H. and Ogura, Y. (2004). Markov or non-Markov property of cM - X processes, J. Math. Soc. Japan, 56, 519-540. MR2048472
    • (2004) J. Math. Soc. Japan , vol.56 , pp. 519-540
    • Matsumoto, H.1    Ogura, Y.2
  • 43
    • 22444456089 scopus 로고    scopus 로고
    • On Bougerol and Dufresne's identity for exponential Brownian functionals
    • Ser.A.
    • Matsumoto, H. and Yor, M. (1998). On Bougerol and Dufresne's identity for exponential Brownian functionals, Proc. Japan Acad., 74 Ser.A., 152- 155.
    • (1998) Proc. Japan Acad. , vol.74
    • Matsumoto, H.1    Yor, M.2
  • 44
    • 0033147983 scopus 로고    scopus 로고
    • A version of Pitman's 2M-X theorem for geometric Brownian motions
    • MR1696208
    • Matsumoto, H. and Yor, M. (1999). A version of Pitman's 2M-X theorem for geometric Brownian motions, C.R. Acad. Sci., Paris, Série I, 328, 1067- 1074. MR1696208
    • (1999) C.R. Acad. Sci., Paris, Série I , vol.328
    • Matsumoto, H.1    Yor, M.2
  • 45
    • 0000131536 scopus 로고    scopus 로고
    • An analogue of Pitman's 2M-X theorem for exponential Wiener functionals, Part I: A time inversion approach
    • MR1783567
    • Matsumoto, H. and Yor, M. (2000). An analogue of Pitman's 2M-X theorem for exponential Wiener functionals, Part I: A time inversion approach, Nagoya Math. J., 159, 125-166. MR1783567
    • (2000) Nagoya Math. J. , vol.159 , pp. 125-166
    • Matsumoto, H.1    Yor, M.2
  • 46
    • 0002855099 scopus 로고    scopus 로고
    • An analogue of Pitman's 2M-X theorem for exponential Wiener functionals, Part II: The role of the generalized Inverse Gaussian laws
    • MR1836133
    • Matsumoto, H. and Yor, M. (2001). An analogue of Pitman's 2M-X theorem for exponential Wiener functionals, Part II: The role of the generalized Inverse Gaussian laws, Nagoya Math. J., 162, 65-86. MR1836133
    • (2001) Nagoya Math. J. , vol.162 , pp. 65-86
    • Matsumoto, H.1    Yor, M.2
  • 47
    • 0001033078 scopus 로고    scopus 로고
    • A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration
    • MR1833628
    • Matsumoto, H. and Yor, M. (2001). A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration, Osaka J. Math., 38, 383-398. MR1833628
    • (2001) Osaka J. Math. , vol.38 , pp. 383-398
    • Matsumoto, H.1    Yor, M.2
  • 48
    • 0037357658 scopus 로고    scopus 로고
    • On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts
    • MR1975510
    • Matsumoto, H. and Yor, M. (2003). On Dufresne's relation between the probability laws of exponential functionals of Brownian motions with different drifts, J. Appl. Prob., 35, 184-206. MR1975510
    • (2003) J. Appl. Prob. , vol.35 , pp. 184-206
    • Matsumoto, H.1    Yor, M.2
  • 49
    • 33745855661 scopus 로고    scopus 로고
    • Exponential Functionals of Brownian motion, I, Probability laws at fixed time
    • Matsumoto, H. and Yor, M. (2005). Exponential Functionals of Brownian motion, I, Probability laws at fixed time, Probab. Surveys, 2, 312-347.
    • (2005) Probab. Surveys , vol.2 , pp. 312-347
    • Matsumoto, H.1    Yor, M.2
  • 50
    • 38249002913 scopus 로고
    • Risk theory in a stochastic economic environment
    • MR1226415
    • Paulsen, J. (1993). Risk theory in a stochastic economic environment, Stoch. Proc. Appl., 46, 327-361. MR1226415
    • (1993) Stoch. Proc. Appl. , vol.46 , pp. 327-361
    • Paulsen, J.1
  • 51
    • 0000884985 scopus 로고
    • One-dimensional Brownian motion and the threedimensional Bessel process
    • MR375485
    • Pitman, J.W. (1975). One-dimensional Brownian motion and the threedimensional Bessel process, Adv. Appl. Prpb., 7, 511-526. MR375485
    • (1975) Adv. Appl. Prpb. , vol.7 , pp. 511-526
    • Pitman, J.W.1
  • 52
    • 0000739144 scopus 로고
    • On nonlinear transformations of Gaussian measures
    • MR349945
    • Ramer, R. (1974). On nonlinear transformations of Gaussian measures, J. Func. Anal., 15, 166-187. MR349945
    • (1974) J. Func. Anal. , vol.15 , pp. 166-187
    • Ramer, R.1
  • 54
    • 0001380232 scopus 로고
    • Markov functions
    • MR624684
    • Rogers, L.C.G. and Pitman, J.W. (1981). Markov functions, Ann. Prob., 9, 573-582. MR624684
    • (1981) Ann. Prob. , vol.9 , pp. 573-582
    • Rogers, L.C.G.1    Pitman, J.W.2
  • 55
    • 21844524143 scopus 로고
    • The value of an Asian option
    • MR1363350
    • Rogers, L.C.G. and Shi, Z. (1995). The value of an Asian option, J. Appl. Prob., 32, 1077-1088. MR1363350
    • (1995) J. Appl. Prob. , vol.32 , pp. 1077-1088
    • Rogers, L.C.G.1    Shi, Z.2
  • 58
    • 0038171245 scopus 로고    scopus 로고
    • A generalization of the Buckdahn-Föllmer formula for composite transformations defined by finite dimensional substitution
    • MR1967053
    • Yano, K. (2002). A generalization of the Buckdahn-Föllmer formula for composite transformations defined by finite dimensional substitution, J. Math. Kyoto Univ., 42, 671-702. MR1967053
    • (2002) J. Math. Kyoto Univ. , vol.42 , pp. 671-702
    • Yano, K.1
  • 61
    • 0012871092 scopus 로고
    • Une extension markovienne de l'algébre des lois bétagamma
    • Yor, M. (1989) Une extension markovienne de l'algébre des lois bétagamma, C.R. Acad. Sci., Paris, Série I, 308, 257-260.
    • (1989) C.R. Acad. Sci., Paris, Série I , vol.308 , pp. 257-260
    • Yor, M.1
  • 62
    • 0000932454 scopus 로고
    • Sur les lois des fonctionnelles exponentielles du mouvement brownien, considérées en certains instants aléatoires
    • C.R. Acad. Sci., Paris, Série I, (Eng. transl. is found in [60].) MR1168332
    • Yor, M. (1992). Sur les lois des fonctionnelles exponentielles du mouvement brownien, considérées en certains instants aléatoires, C.R. Acad. Sci., Paris, Série I, 314, 951-956. (Eng. transl. is found in [60].) MR1168332
    • (1992) , vol.314 , pp. 951-956
    • Yor, M.1
  • 63
    • 0000364811 scopus 로고
    • On some exponential functionals of Brownian motion
    • (also found in [60].) MR1174378
    • Yor, M. (1992). On some exponential functionals of Brownian motion, Adv. Appl. Prob., 24, 509-531. (also found in [60].) MR1174378
    • (1992) Adv. Appl. Prob. , vol.24 , pp. 509-531
    • Yor, M.1
  • 64
    • 0040936534 scopus 로고    scopus 로고
    • Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity
    • eds. O.E.Barndorff-Nielsen, T.Mikosch and S.I.Resnick, Birkhäser. MR1833705
    • Yor, M. (2001). Interpretations in terms of Brownian and Bessel meanders of the distribution of a subordinated perpetuity, in Lévy Processes, Theory and Applications, 361-375, eds. O.E.Barndorff-Nielsen, T.Mikosch and S.I.Resnick, Birkhäser. MR1833705
    • (2001) in Lévy Processes, Theory and Applications , pp. 361-375
    • Yor, M.1
  • 65
    • 0003912433 scopus 로고    scopus 로고
    • Exponential Functionals and Principal Values related to Brownian Motion
    • (Ed.), A collection of research papers, Biblioteca de la Revista Matemática Iberoamericana. MR1648653
    • Yor, M. (Ed.) (1997). Exponential Functionals and Principal Values related to Brownian Motion, A collection of research papers, Biblioteca de la Revista Matemática Iberoamericana. MR1648653
    • (1997)
    • Yor, M.1


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