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Volumn 41, Issue 3 SPEC. ISS., 2005, Pages 335-347

Properties of perpetual integral functionals of Brownian motion with drift

Author keywords

Green function; Kac's moment formula; Khas'minskii's lemma; Last exit time; Local time

Indexed keywords


EID: 17544366163     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2004.01.006     Document Type: Article
Times cited : (34)

References (30)
  • 1
    • 0003359661 scopus 로고    scopus 로고
    • Subordinators: Examples and applications
    • J. Bertoin F. Martinelli Y. Peres (Eds.) École d'eté de Probabilités de Saint-Flour XXVII-1997 Springer Berlin
    • J. Bertoin Subordinators: Examples and applications in: J. Bertoin F. Martinelli Y. Peres (Eds.) École d'eté de Probabilités de Saint-Flour XXVII-1997 in: Lecture Notes in Math. vol. 1717 1999 Springer Berlin 1-91
    • (1999) Lecture Notes in Math. , vol.1717 , pp. 1-91
    • Bertoin, J.1
  • 3
    • 23044525613 scopus 로고    scopus 로고
    • Convergence of some integrals associated with Bessel processes
    • A.S. Cherny Convergence of some integrals associated with Bessel processes Theoret. Probab. Appl. 45 2000 251-267
    • (2000) Theoret. Probab. Appl. , vol.45 , pp. 251-267
    • Cherny, A.S.1
  • 5
    • 0000651517 scopus 로고
    • Convergence of integrals of uniform empirical and quantile processes
    • M. Csörgö L. Horváth Q.M. Shao Convergence of integrals of uniform empirical and quantile processes Stochastic Process. Appl. 45 1993 278-294
    • (1993) Stochastic Process. Appl. , vol.45 , pp. 278-294
    • Csörgö, M.1    Horváth, L.2    Shao, Q.M.3
  • 7
    • 84864849879 scopus 로고
    • The distribution of a perpetuity, with applications to risk theory and pension funding
    • D. Dufresne The distribution of a perpetuity, with applications to risk theory and pension funding Scand. Actuar. J. 1-2 1990 39-79
    • (1990) Scand. Actuar. J. , vol.1-2 , pp. 39-79
    • Dufresne, D.1
  • 9
    • 0042110035 scopus 로고
    • Une définition faible de BMO
    • M. Emery Une définition faible de BMO Ann. Inst. H. Poincare 21 1985 59-72
    • (1985) Ann. Inst. H. Poincare , vol.21 , pp. 59-72
    • Emery, M.1
  • 10
    • 0001916270 scopus 로고
    • On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations
    • Stochastic Differential Systems. Proc. 3rd IFIP-WG 7/1 Working Conf. Springer-Verlag Berlin
    • H.J. Engelbert W. Schmidt On the behaviour of certain functionals of the Wiener process and applications to stochastic differential equations in: Stochastic Differential Systems. Proc. 3rd IFIP-WG 7/1 Working Conf. in: Lecture Notes in Control and Inform. Sci. vol. 36 1981 Springer-Verlag Berlin 47-55
    • (1981) Lecture Notes in Control and Inform. Sci. , vol.36 , pp. 47-55
    • Engelbert, H.J.1    Schmidt, W.2
  • 11
    • 84985400066 scopus 로고
    • On exponential local martingales connected with diffusion processes
    • H.J. Engelbert W. Schmidt On exponential local martingales connected with diffusion processes Math. Nachr. 119 1984 97-115
    • (1984) Math. Nachr. , vol.119 , pp. 97-115
    • Engelbert, H.J.1    Schmidt, W.2
  • 12
    • 0007224145 scopus 로고
    • On the behaviour of certain Bessel functionals. An application to a class of stochastic differential equations
    • H.J. Engelbert W. Schmidt On the behaviour of certain Bessel functionals. An application to a class of stochastic differential equations Math. Nachr. 131 1987 219-234
    • (1987) Math. Nachr. , vol.131 , pp. 219-234
    • Engelbert, H.J.1    Schmidt, W.2
  • 13
    • 17544382186 scopus 로고
    • On functionals of Wiener process with drift and exponential local martingales
    • M. Dozzi H.J. Engelbert D. Nualart (Eds.) Stochastic Processes and Related Topics, Proc. Wintersch. Stochastic Processes, Optim. Control, Georgenthal/Ger. 1990 Academic-Verlag Berlin
    • H.J. Engelbert T. Senf On functionals of Wiener process with drift and exponential local martingales in: M. Dozzi H.J. Engelbert D. Nualart (Eds.) Stochastic Processes and Related Topics, Proc. Wintersch. Stochastic Processes, Optim. Control, Georgenthal/Ger. 1990 in: Math. Res. vol. 61 1991 Academic-Verlag Berlin 45-58
    • (1991) Math. Res. , vol.61 , pp. 45-58
    • Engelbert, H.J.1    Senf, T.2
  • 14
    • 0011975680 scopus 로고    scopus 로고
    • Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process
    • P. Fitzsimmons J. Pitman Kac's moment formula and the Feynman-Kac formula for additive functionals of a Markov process Stochastic Process. Appl. 79 1999 117-134
    • (1999) Stochastic Process. Appl. , vol.79 , pp. 117-134
    • Fitzsimmons, P.1    Pitman, J.2
  • 15
    • 0003343220 scopus 로고
    • Semimartingales et grossissement d'une filtration
    • Berlin: Springer-Verlag
    • T. Jeulin Semimartingales et grossissement d'une filtration Lecture Notes in Math. vol. 833 1980 Springer-Verlag Berlin
    • (1980) Lecture Notes in Math. , vol.833
    • Jeulin, T.1
  • 16
    • 0007388439 scopus 로고
    • Sur la convergence absolue de certaines intégrales
    • J. Azéma M. Yor (Eds.) Séminaire de Probabilités XVI Springer Berlin
    • T. Jeulin Sur la convergence absolue de certaines intégrales in: J. Azéma M. Yor (Eds.) Séminaire de Probabilités XVI Lecture Notes in Math. vol. 920 1982 Springer Berlin 248-256
    • (1982) Lecture Notes in Math. , vol.920 , pp. 248-256
    • Jeulin, T.1
  • 17
    • 0003224552 scopus 로고
    • Continuous Exponential Martigales and BMO
    • Berlin: Springer-Verlag
    • N. Kazamaki Continuous Exponential Martigales and BMO Lecture Notes in Math. vol. 1579 1994 Springer-Verlag Berlin
    • (1994) Lecture Notes in Math. , vol.1579
    • Kazamaki, N.1
  • 18
    • 84972548797 scopus 로고
    • On the transformation of some classes of martingales by a change of law
    • N. Kazamaki T. Sekiguchi On the transformation of some classes of martingales by a change of law Tôhoku Math. J. 31 1979 261-279
    • (1979) Tôhoku Math. J. , vol.31 , pp. 261-279
    • Kazamaki, N.1    Sekiguchi, T.2
  • 19
    • 0000612703 scopus 로고
    • On positive solutions of the equation Au + Vu = 0
    • R. Khas'minskii On positive solutions of the equation Au + Vu = 0 Theoret. Probab. Appl. 4 1959 309-318
    • (1959) Theoret. Probab. Appl. , vol.4 , pp. 309-318
    • Khas'minskii, R.1
  • 21
    • 0001452295 scopus 로고
    • Bessel processes and infinitely divisible laws
    • D. Williams (Ed.) Stochastic Integrals Springer-Verlag Berlin
    • J. Pitman M. Yor Bessel processes and infinitely divisible laws in: D. Williams (Ed.) Stochastic Integrals in: Lecture Notes in Math. vol. 851 1981 Springer-Verlag Berlin 285-370
    • (1981) Lecture Notes in Math. , vol.851 , pp. 285-370
    • Pitman, J.1    Yor, M.2
  • 23
    • 0000798846 scopus 로고
    • Some divergent integrals of Brownian motion
    • D. Kendall (Ed.) Analytic and Geometric Stochastics
    • J. Pitman M. Yor Some divergent integrals of Brownian motion in: D. Kendall (Ed.) Analytic and Geometric Stochastics Adv. Appl. Probab. Supplement 1986 109-116
    • (1986) Adv. Appl. Probab. , Issue.SUPPL. , pp. 109-116
    • Pitman, J.1    Yor, M.2
  • 24
    • 17544378154 scopus 로고    scopus 로고
    • Perpetual integral functionals as hitting times
    • in press
    • P. Salminen, M. Yor, Perpetual integral functionals as hitting times, Elec. J. Prob., in press
    • Elec. J. Prob.
    • Salminen, P.1    Yor, M.2
  • 25
    • 0000730931 scopus 로고
    • Radon-Nikodym derivatives of Gaussian measures
    • L.A. Shepp Radon-Nikodym derivatives of Gaussian measures Ann. Math. Statist. 37 1966 321-354
    • (1966) Ann. Math. Statist. , vol.37 , pp. 321-354
    • Shepp, L.A.1
  • 27
    • 0005508708 scopus 로고    scopus 로고
    • On exponentials of additive functionals of Markov processes
    • W. Stummer K.-T. Sturm On exponentials of additive functionals of Markov processes Stochastic Process. Appl. 85 2000 45-60
    • (2000) Stochastic Process. Appl. , vol.85 , pp. 45-60
    • Stummer, W.1    Sturm, K.-T.2
  • 28
    • 0040949451 scopus 로고
    • A zero-one law for integral functionals of the Bessel process
    • J. Azéma P.A. Meyer M. Yor (Eds.) Séminaire de Probabilités XXIV Springer Berlin
    • X.-X. Xue A zero-one law for integral functionals of the Bessel process in: J. Azéma P.A. Meyer M. Yor (Eds.) Séminaire de Probabilités XXIV in: Lecture Notes in Math. vol. 1426 1990 Springer Berlin 137-153
    • (1990) Lecture Notes in Math. , vol.1426 , pp. 137-153
    • Xue, X.-X.1
  • 29
    • 0000300111 scopus 로고
    • Sur certaines fonctionnelles exponentielles du mouvement brownien réel
    • M. Yor Sur certaines fonctionnelles exponentielles du mouvement brownien réel J. Appl. Probab. 29 1992 202-208
    • (1992) J. Appl. Probab. , vol.29 , pp. 202-208
    • Yor, M.1
  • 30
    • 0003632582 scopus 로고    scopus 로고
    • Exponential Functionals of Brownian Motion and Related Processes
    • Berlin: Springer-Verlag
    • M. Yor Exponential Functionals of Brownian Motion and Related Processes Springer Finance 2001 Springer-Verlag Berlin
    • (2001) Springer Finance
    • Yor, M.1


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