M. Yor :
“Loi de l’indice du lacet brownien, et distribution de Hartman–Watson ”
[Law of indices of Brownian laces, and the Hartman–Watson distribution ],
Z. Wahrscheinlichkeitstheor. Verw. Geb.
53 : 1
(January 1980 ),
pp. 71–95 .
MR
576898
Zbl
0436.60057
article
BibTeX
@article {key576898m,
AUTHOR = {Yor, Marc},
TITLE = {Loi de l'indice du lacet brownien, et
distribution de {H}artman--{W}atson
[Law of indices of {B}rownian laces,
and the {H}artman--{W}atson distribution]},
JOURNAL = {Z. Wahrscheinlichkeitstheor. Verw. Geb.},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {53},
NUMBER = {1},
MONTH = {January},
YEAR = {1980},
PAGES = {71--95},
DOI = {10.1007/BF00531612},
NOTE = {MR:576898. Zbl:0436.60057.},
ISSN = {0044-3719},
}
J. Pitman and M. Yor :
“Bessel processes and infinitely divisible laws ,”
pp. 285–370
in
Stochastic integrals
(Durham, UK, 7–17 July 1980 ).
Edited by D. Williams .
Lecture Notes in Mathematics 851 .
Springer (Berlin ),
1981 .
MR
620995
Zbl
0469.60076
incollection
People
BibTeX
@incollection {key620995m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {Bessel processes and infinitely divisible
laws},
BOOKTITLE = {Stochastic integrals},
EDITOR = {Williams, David},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {851},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
PAGES = {285--370},
DOI = {10.1007/BFb0088732},
NOTE = {(Durham, UK, 7--17 July 1980). MR:620995.
Zbl:0469.60076.},
ISSN = {0075-8434},
ISBN = {9783540106906},
}
J. Pitman and M. Yor :
“A decomposition of Bessel bridges ,”
Z. Wahrsch. Verw. Gebiete
59 : 4
(December 1982 ),
pp. 425–457 .
English translation of French original from Functional analysis in Markov processes (1982) .
MR
656509
Zbl
0484.60062
article
People
BibTeX
@article {key656509m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {A decomposition of {B}essel bridges},
JOURNAL = {Z. Wahrsch. Verw. Gebiete},
FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie
und Verwandte Gebiete},
VOLUME = {59},
NUMBER = {4},
MONTH = {December},
YEAR = {1982},
PAGES = {425--457},
DOI = {10.1007/BF00532802},
NOTE = {English translation of French original
from \textit{Functional analysis in
Markov processes} (1982). MR:656509.
Zbl:0484.60062.},
ISSN = {0044-3719},
}
P. Messulam and M. Yor :
“D. Williams’ ‘pinching method’ and some applications ,”
J. Lond. Math. Soc., II. Ser.
26 : 2
(1982 ),
pp. 348–364 .
MR
675178
Zbl
0518.60088
article
BibTeX
@article {key675178m,
AUTHOR = {Messulam, P. and Yor, M.},
TITLE = {D. {W}illiams' ``pinching method'' and
some applications},
JOURNAL = {J. Lond. Math. Soc., II. Ser.},
FJOURNAL = {The Journal of the London Mathematical
Society. Second Series},
VOLUME = {26},
NUMBER = {2},
YEAR = {1982},
PAGES = {348--364},
DOI = {10.1112/jlms/s2-26.2.348},
NOTE = {MR:675178. Zbl:0518.60088.},
ISSN = {0024-6107},
}
J.-F. Le Gall and M. Yor :
“Étude asymptotique de certains mouvements browniens complexes avec drift ”
[Asymptotic study of certain complex Brownian motions with drift ],
Probab. Theory Relat. Fields
71 : 2
(January 1986 ),
pp. 183–229 .
MR
816704
Zbl
0579.60077
article
People
BibTeX
@article {key816704m,
AUTHOR = {Le Gall, J.-F. and Yor, M.},
TITLE = {\'{E}tude asymptotique de certains mouvements
browniens complexes avec drift [Asymptotic
study of certain complex {B}rownian
motions with drift]},
JOURNAL = {Probab. Theory Relat. Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {71},
NUMBER = {2},
MONTH = {January},
YEAR = {1986},
PAGES = {183--229},
DOI = {10.1007/BF00332310},
NOTE = {MR:816704. Zbl:0579.60077.},
ISSN = {0178-8051},
}
J. Pitman and M. Yor :
“Asymptotic laws of planar Brownian motion ,”
Ann. Probab.
14 : 3
(1986 ),
pp. 733–779 .
A follow-up to this was published in Ann. Probab. 17 :3 (1989) .
MR
841582
Zbl
0607.60070
article
Abstract
People
BibTeX
Recent results on the asymptotic distribution of winding and crossing numbers are presented as part of a larger framework of asymptotic laws for planar Brownian motion. The approach is via random time changes, martingale calculus, and excursion theory.
@article {key841582m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {Asymptotic laws of planar {B}rownian
motion},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {14},
NUMBER = {3},
YEAR = {1986},
PAGES = {733--779},
DOI = {10.1214/aop/1176992436},
NOTE = {A follow-up to this was published in
\textit{Ann. Probab.} \textbf{17}:3
(1989). MR:841582. Zbl:0607.60070.},
ISSN = {0091-1798},
}
J. Pitman and M. Yor :
“Level crossings of a Cauchy process ,”
Ann. Probab.
14 : 3
(1986 ),
pp. 780–792 .
MR
841583
Zbl
0602.60059
article
Abstract
People
BibTeX
The asymptotic distribution as \( t\to\infty \) is obtained for the number of jumps of a symmetric Cauchy process across level \( x \) up to time \( t \) , jointly as \( x \) varies. This result is related to the asymptotic joint distribution of windings of a planar Brownian motion about several points.
@article {key841583m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {Level crossings of a {C}auchy process},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {14},
NUMBER = {3},
YEAR = {1986},
PAGES = {780--792},
DOI = {10.1214/aop/1176992437},
URL = {https://www.jstor.org/stable/2244133},
NOTE = {MR:841583. Zbl:0602.60059.},
ISSN = {0091-1798},
}
J.-F. Le Gall and M. Yor :
“Étude asymptotique des enlacements du mouvement brownien autour des droites de l’espace ”
[Asymptotic study of windings of Brownian motion around straight lines ],
Probab. Theory Relat. Fields
74 : 4
(April 1987 ),
pp. 617–635 .
MR
876259
Zbl
0594.60083
article
People
BibTeX
@article {key876259m,
AUTHOR = {Le Gall, J.-F. and Yor, M.},
TITLE = {\'{E}tude asymptotique des enlacements
du mouvement brownien autour des droites
de l'espace [Asymptotic study of windings
of {B}rownian motion around straight
lines]},
JOURNAL = {Probab. Theory Relat. Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {74},
NUMBER = {4},
MONTH = {April},
YEAR = {1987},
PAGES = {617--635},
DOI = {10.1007/BF00363519},
NOTE = {MR:876259. Zbl:0594.60083.},
ISSN = {0178-8051},
}
J. Pitman and M. Yor :
“Further asymptotic laws of planar Brownian motion ,”
Ann. Probab.
17 : 3
(1989 ),
pp. 965–1011 .
This was a follow-up to an article published in Ann. Probab. 14 :3 (1986) .
MR
1009441
Zbl
0686.60085
article
People
BibTeX
@article {key1009441m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {Further asymptotic laws of planar {B}rownian
motion},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {17},
NUMBER = {3},
YEAR = {1989},
PAGES = {965--1011},
DOI = {10.1214/aop/1176991253},
NOTE = {This was a follow-up to an article published
in \textit{Ann. Probab.} \textbf{14}:3
(1986). MR:1009441. Zbl:0686.60085.},
ISSN = {0091-1798},
}
J.-F. Le Gall and M. Yor :
“Enlacements du mouvement brownien autour des courbes de l’espace ”
[Winding of Brownian motion around space curves ],
Trans. Am. Math. Soc.
317 : 2
(February 1990 ),
pp. 687–722 .
MR
946219
Zbl
0696.60072
article
Abstract
People
BibTeX
Limit theorems are proved for the winding numbers of a three-dimensional Brownian motion around certain curves in space. In particular, the joint asymptotic distribution of the winding numbers around two curves is obtained. This joint distribution generalizes the asymptotic law of the winding numbers of a planar Brownian motion around two points, which has recently been given by Pitman and Yor. The limiting distributions are closely related to the time spent by a linear Brownian motion above and below a multiple of its maximum process. Proofs rely on stochastic calculus for continuous semi-martingales.
@article {key946219m,
AUTHOR = {Le Gall, Jean-Fran\c{c}ois and Yor,
Marc},
TITLE = {Enlacements du mouvement brownien autour
des courbes de l'espace [Winding of
{B}rownian motion around space curves]},
JOURNAL = {Trans. Am. Math. Soc.},
FJOURNAL = {Transactions of the American Mathematical
Society},
VOLUME = {317},
NUMBER = {2},
MONTH = {February},
YEAR = {1990},
PAGES = {687--722},
DOI = {10.2307/2001484},
NOTE = {MR:946219. Zbl:0696.60072.},
ISSN = {0002-9947},
}
D. Revuz and M. Yor :
Continuous martingales and Brownian motion .
Grundlehren der Mathematischen Wissenschaften 293 .
Springer (Berlin ),
1991 .
A 2nd edition was published in 1994 . A 3rd edition was published in 1999 .
MR
1083357
Zbl
0731.60002
book
People
BibTeX
@book {key1083357m,
AUTHOR = {Revuz, Daniel and Yor, Marc},
TITLE = {Continuous martingales and {B}rownian
motion},
SERIES = {Grundlehren der Mathematischen Wissenschaften},
NUMBER = {293},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1991},
PAGES = {x+533},
DOI = {10.1007/978-3-662-21726-9},
NOTE = {A 2nd edition was published in 1994.
A 3rd edition was published in 1999.
MR:1083357. Zbl:0731.60002.},
ISSN = {0072-7830},
ISBN = {9783662217283},
}
M. Yor :
Some aspects of Brownian motion ,
part 1: Some special functionals .
Lectures in Mathematics ETH Zürich .
Birkhäuser (Basel ),
1992 .
MR
1193919
Zbl
0779.60070
book
BibTeX
@book {key1193919m,
AUTHOR = {Yor, Marc},
TITLE = {Some aspects of {B}rownian motion},
VOLUME = {1: Some special functionals},
SERIES = {Lectures in Mathematics ETH Z\"urich},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Basel},
YEAR = {1992},
PAGES = {x+136},
NOTE = {MR:1193919. Zbl:0779.60070.},
ISBN = {9783764328078},
}