메뉴 건너뛰기




Volumn 26, Issue 4, 1998, Pages 1683-1702

Random Brownian scaling identities and splicing of Bessel processes

Author keywords

Bessel process; Brownian bridge; Brownian excursion; Brownian scaling; Local time; Path transformation; Range process; Williams' decomposition

Indexed keywords


EID: 0032245847     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (13)

References (38)
  • 1
    • 0002283157 scopus 로고
    • Relations entre pont et excursion du mouvement Brownien réel
    • BIANE, P. (1986). Relations entre pont et excursion du mouvement Brownien réel. Ann. Inst. H. Poincaré 22 1-7.
    • (1986) Ann. Inst. H. Poincaré , vol.22 , pp. 1-7
    • Biane, P.1
  • 4
    • 0002859752 scopus 로고
    • Valeurs principales associées aux temps locaux Browniens
    • BIANE, P. and YOR, M. (1987). Valeurs principales associées aux temps locaux Browniens. Bull. Sci. Math. 111 23-101.
    • (1987) Bull. Sci. Math. , vol.111 , pp. 23-101
    • Biane, P.1    Yor, M.2
  • 5
    • 0002306415 scopus 로고
    • Last exit decompositions and regularity at the boundary of transition probabilities
    • BISMUT, J.-M. (1985). Last exit decompositions and regularity at the boundary of transition probabilities. Z. Wahrsch. Verw. Gebiete. 69 65-98.
    • (1985) Z. Wahrsch. Verw. Gebiete. , vol.69 , pp. 65-98
    • Bismut, J.-M.1
  • 6
    • 21844483926 scopus 로고
    • Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion
    • CARMONA, P., PETIT, F. and YOR, M. (1994). Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion. Probab. Theory Related Fields. 100 1-29.
    • (1994) Probab. Theory Related Fields. , vol.100 , pp. 1-29
    • Carmona, P.1    Petit, F.2    Yor, M.3
  • 8
    • 0001186590 scopus 로고
    • The Brownian escape process
    • GETOOR, R. K. (1979). The Brownian escape process. Ann. Probab. 7 864-867.
    • (1979) Ann. Probab. , vol.7 , pp. 864-867
    • Getoor, R.K.1
  • 11
    • 0001050284 scopus 로고
    • Poisson point processes attached to Markov processes
    • Univ. California Press, Berkeley
    • ITÔ, K. (1971). Poisson point processes attached to Markov processes. Proc. Sixth Berkley Symp. Math. Statist. Probab. 3 225-240. Univ. California Press, Berkeley.
    • (1971) Proc. Sixth Berkley Symp. Math. Statist. Probab. , vol.3 , pp. 225-240
    • Itô, K.1
  • 12
    • 0009153241 scopus 로고    scopus 로고
    • The Feynman-Kac formula and decomposition of Brownian paths
    • JEANBLANC, M., PITMAN, J. and YOR, M. (1997). The Feynman-Kac formula and decomposition of Brownian paths. Comput. Appl. Math. 16 27-52.
    • (1997) Comput. Appl. Math. , vol.16 , pp. 27-52
    • Jeanblanc, M.1    Pitman, J.2    Yor, M.3
  • 13
    • 0001251792 scopus 로고
    • Some probabilistic properties of Bessel functions
    • KENT, J. (1978). Some probabilistic properties of Bessel functions. Ann. Probab. 6 760-770.
    • (1978) Ann. Probab. , vol.6 , pp. 760-770
    • Kent, J.1
  • 15
    • 0000944515 scopus 로고
    • Symmetric stable processes as traces of degenerate diffusion processes
    • MOLCHANOV, S. A. and OSTROVSKI, E. (1969). Symmetric stable processes as traces of degenerate diffusion processes. Theory Probab. Appl. 14 128-131.
    • (1969) Theory Probab. Appl. , vol.14 , pp. 128-131
    • Molchanov, S.A.1    Ostrovski, E.2
  • 17
    • 0000884210 scopus 로고    scopus 로고
    • Cyclically stationary Brownian local time processes
    • PITMAN, J. (1996). Cyclically stationary Brownian local time processes. Probab. Theory Related Fields 106 299-329.
    • (1996) Probab. Theory Related Fields , vol.106 , pp. 299-329
    • Pitman, J.1
  • 18
    • 0000674721 scopus 로고
    • A decomposition of Bessel bridges
    • PITMAN, J. and YOR, M. (1982). A decomposition of Bessel bridges. Z. Wahrsch. Verw. Gebiete 59 425-457.
    • (1982) Z. Wahrsch. Verw. Gebiete , vol.59 , pp. 425-457
    • Pitman, J.1    Yor, M.2
  • 19
    • 84962993911 scopus 로고
    • Arcsine laws and interval partitions derived from a stable subordinator
    • PITMAN, J. and YOR, M. (1992). Arcsine laws and interval partitions derived from a stable subordinator. Proc. London Math. Soc. 3 65 326-356.
    • (1992) Proc. London Math. Soc. 3 , vol.65 , pp. 326-356
    • Pitman, J.1    Yor, M.2
  • 20
    • 0010912953 scopus 로고
    • Dilatations d'espace-temps, réarrangements des trajectoires browniennes, et quelques extensions d'une identité de Knight
    • PITMAN, J. and YOR, M. (1993). Dilatations d'espace-temps, réarrangements des trajectoires browniennes, et quelques extensions d'une identité de Knight. C.R. Acad. Sci. Paris Ser. I Math. 316 723-726.
    • (1993) C.R. Acad. Sci. Paris Ser. I Math. , vol.316 , pp. 723-726
    • Pitman, J.1    Yor, M.2
  • 21
    • 0002975171 scopus 로고    scopus 로고
    • Decomposition at the maximum for excursions and bridges of one-dimensional diffusions
    • (N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita, eds.) Springer, New York
    • PITMAN, J. and YOR, M. (1996). Decomposition at the maximum for excursions and bridges of one-dimensional diffusions. In Itô's Stochastic Calculus and Probability Theory (N. Ikeda, S. Watanabe, M. Fukushima and H. Kunita, eds.) 293-310. Springer, New York.
    • (1996) Itô's Stochastic Calculus and Probability Theory , pp. 293-310
    • Pitman, J.1    Yor, M.2
  • 22
    • 0001280730 scopus 로고    scopus 로고
    • On the relative lengths of excursions derived from a stable subordinator
    • Springer, Berlin
    • PITMAN, J. and YOR, M. (1997). On the relative lengths of excursions derived from a stable subordinator. Séminaire de Probabilités XXXI Lecture Notes in Math. 1655 287-305. Springer, Berlin.
    • (1997) Séminaire de Probabilités XXXI Lecture Notes in Math. , vol.1655 , pp. 287-305
    • Pitman, J.1    Yor, M.2
  • 23
    • 0031534984 scopus 로고    scopus 로고
    • The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
    • PITMAN, J. and YOR, M. (1997). The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator. Ann. Probab. 25 855-900.
    • (1997) Ann. Probab. , vol.25 , pp. 855-900
    • Pitman, J.1    Yor, M.2
  • 27
    • 0002115073 scopus 로고
    • Bessel diffusions as a one-parameter family of diffusion processes
    • SHIGA, T. and WATANABE, S. (1973). Bessel diffusions as a one-parameter family of diffusion processes. Z. Wahrsch. Verw. Gebiete 27 37-46.
    • (1973) Z. Wahrsch. Verw. Gebiete , vol.27 , pp. 37-46
    • Shiga, T.1    Watanabe, S.2
  • 28
    • 0041028657 scopus 로고
    • Sur la loi conjointe du maximum et de l'inverse du temps local du mouvement brownien: Applications à un théorème de Knight
    • VALLOIS, P. (1991). Sur la loi conjointe du maximum et de l'inverse du temps local du mouvement brownien: applications à un théorème de Knight. Stochastics Stochastics Rep. 35 175-186.
    • (1991) Stochastics Stochastics Rep. , vol.35 , pp. 175-186
    • Vallois, P.1
  • 29
    • 0010018516 scopus 로고
    • Decomposing the Brownian path via the range process
    • VALLOIS, P. (1995). Decomposing the Brownian path via the range process. Stochastic Process. Appl. 55 211-226.
    • (1995) Stochastic Process. Appl. , vol.55 , pp. 211-226
    • Vallois, P.1
  • 30
    • 0000246649 scopus 로고
    • A relation between Brownian bridge and Brownian excursion
    • VERVAAT, W. (1979). A relation between Brownian bridge and Brownian excursion. Ann. Probab. 7 143-149.
    • (1979) Ann. Probab. , vol.7 , pp. 143-149
    • Vervaat, W.1
  • 32
    • 84966207775 scopus 로고
    • Decomposing the Brownian path
    • WILLIAMS, D. (1970). Decomposing the Brownian path. Bull. Amer. Math. Soc. 76 871-873.
    • (1970) Bull. Amer. Math. Soc. , vol.76 , pp. 871-873
    • Williams, D.1
  • 33
    • 33749017547 scopus 로고
    • Path decomposition and continuity of local time for one dimensional diffusions I
    • WILLIAMS, D. (1974). Path decomposition and continuity of local time for one dimensional diffusions I. Proc. London Math. Soc. 3 28 738-768.
    • (1974) Proc. London Math. Soc. 3 , vol.28 , pp. 738-768
    • Williams, D.1
  • 35
    • 0007435241 scopus 로고
    • Brownian motion and the Riemann zeta-function
    • (G. R. Grimmett and D. J. A. Welsh, eds.) Clarendon Press, Oxford
    • WILLIAMS, D. (1990). Brownian motion and the Riemann zeta-function. In Disorder in Physical Systems (G. R. Grimmett and D. J. A. Welsh, eds.) 361-372. Clarendon Press, Oxford.
    • (1990) Disorder in Physical Systems , pp. 361-372
    • Williams, D.1
  • 37
    • 0040252711 scopus 로고
    • Random Brownian scaling and some absolute continuity relationships
    • (E. Bolthausen, M. Dozzi, and F. Russo, eds.) Birkhäuser, Boston
    • YOR, M. (1995). Random Brownian scaling and some absolute continuity relationships. In Seminar on Stochastic Analysis, Random Fields and Applications (E. Bolthausen, M. Dozzi, and F. Russo, eds.) 243-252. Birkhäuser, Boston.
    • (1995) Seminar on Stochastic Analysis, Random Fields and Applications , pp. 243-252
    • Yor, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.