P. Biane and M. Yor :
“Valeurs principales associées aux temps locaux browniens et processus stables symétriques ”
[Principal values associated with Brownian local times and stable symmetric processes ],
C. R. Acad. Sci., Paris, Sér. I
300 : 20
(1985 ),
pp. 695–698 .
MR
799465
Zbl
0583.60080
article
People
BibTeX
@article {key799465m,
AUTHOR = {Biane, Philippe and Yor, Marc},
TITLE = {Valeurs principales associ\'ees aux
temps locaux browniens et processus
stables sym\'etriques [Principal values
associated with {B}rownian local times
and stable symmetric processes]},
JOURNAL = {C. R. Acad. Sci., Paris, S\'er. I},
FJOURNAL = {Comptes Rendus des S\'eances de l'Acad\'emie
des Sciences. S\'erie I. Math\'ematique},
VOLUME = {300},
NUMBER = {20},
YEAR = {1985},
PAGES = {695--698},
NOTE = {MR:799465. Zbl:0583.60080.},
ISSN = {0249-6291},
}
P. Biane and M. Yor :
“Valeurs principales associées aux temps locaux browniens ”
[Principal values associated to Brownian local times ],
Bull. Sci. Math., II. Sér.
111 : 1
(1987 ),
pp. 23–101 .
MR
886959
Zbl
0619.60072
article
People
BibTeX
@article {key886959m,
AUTHOR = {Biane, Ph. and Yor, M.},
TITLE = {Valeurs principales associ\'ees aux
temps locaux browniens [Principal values
associated to {B}rownian local times]},
JOURNAL = {Bull. Sci. Math., II. S\'er.},
FJOURNAL = {Bulletin des Sciences Math\'ematiques.
2e S\'erie},
VOLUME = {111},
NUMBER = {1},
YEAR = {1987},
PAGES = {23--101},
NOTE = {MR:886959. Zbl:0619.60072.},
ISSN = {0007-4497},
}
P. Biane and M. Yor :
“Variations sur une formule de Paul Lévy ”
[Variations on a formula of Paul Lévy ],
Ann. Inst. Henri Poincaré, Probab. Stat.
23 : S2
(1987 ),
pp. 359–377 .
MR
898500
Zbl
0623.60099
article
People
BibTeX
@article {key898500m,
AUTHOR = {Biane, Ph. and Yor, M.},
TITLE = {Variations sur une formule de {P}aul
{L}\'evy [Variations on a formula of
{P}aul {L}\'evy]},
JOURNAL = {Ann. Inst. Henri Poincar\'e, Probab.
Stat.},
FJOURNAL = {Annales de l'Institut Henri Poincar\'e.
Probabilit\'es et Statistique},
VOLUME = {23},
NUMBER = {S2},
YEAR = {1987},
PAGES = {359--377},
URL = {http://www.numdam.org/item/AIHPB_1987__23_S2_359_0/},
NOTE = {MR:898500. Zbl:0623.60099.},
ISSN = {0246-0203},
}
P. Biane, J.-F. Le Gall, and M. Yor :
“Un processus qui ressemble au pont brownien ”
[A process that resembles the Brownian bridge ],
pp. 270–275
in
Séminaire de probabilités XXI
[Twenty-first probability seminar ].
Edited by J. Az’e\ma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1247 .
Springer (Berlin ),
1987 .
MR
941990
Zbl
0621.60086
incollection
People
BibTeX
@incollection {key941990m,
AUTHOR = {Biane, Ph. and Le Gall, J.-F. and Yor,
M.},
TITLE = {Un processus qui ressemble au pont brownien
[A process that resembles the {B}rownian
bridge]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXI}
[Twenty-first probability seminar]},
EDITOR = {Az'e\ma, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1247},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1987},
PAGES = {270--275},
DOI = {10.1007/BFb0077641},
URL = {http://www.numdam.org/item?id=SPS_1987__21__270_0},
NOTE = {MR:941990. Zbl:0621.60086.},
ISSN = {0075-8434},
ISBN = {9783540177685},
}
P. Biane and M. Yor :
“Quelques précisions sur le méandre brownien ”
[Some details on the Brownian meander ],
Bull. Sci. Math., II. Sér.
112 : 1
(1988 ),
pp. 101–109 .
MR
942801
Zbl
0665.60081
article
People
BibTeX
@article {key942801m,
AUTHOR = {Biane, Ph. and Yor, M.},
TITLE = {Quelques pr\'ecisions sur le m\'eandre
brownien [Some details on the {B}rownian
meander]},
JOURNAL = {Bull. Sci. Math., II. S\'er.},
FJOURNAL = {Bulletin des Sciences Math\'ematiques.
2e S\'erie},
VOLUME = {112},
NUMBER = {1},
YEAR = {1988},
PAGES = {101--109},
NOTE = {MR:942801. Zbl:0665.60081.},
ISSN = {0007-4497},
}
P. Biane and M. Yor :
“Sur la loi des temps locaux browniens pris en un temps exponentiel ”
[On the law of Brownian local times at an exponential time ],
pp. 454–466
in
Séminaire de probabilités XXII
[Twenty-second probability seminar ].
Edited by J. Azéma, P. A. Meyer, and M. Yor .
Lecture Notes in Mathematics 1321 .
Springer (Berlin ),
1988 .
MR
960541
Zbl
0652.60081
incollection
People
BibTeX
@incollection {key960541m,
AUTHOR = {Biane, Ph. and Yor, M.},
TITLE = {Sur la loi des temps locaux browniens
pris en un temps exponentiel [On the
law of {B}rownian local times at an
exponential time]},
BOOKTITLE = {S\'eminaire de probabilit\'es {XXII}
[Twenty-second probability seminar]},
EDITOR = {Az\'ema, J. and Meyer, P. A. and Yor,
M.},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {1321},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1988},
PAGES = {454--466},
DOI = {10.1007/BFb0084151},
URL = {http://www.numdam.org/item?id=SPS_1988__22__454_0},
NOTE = {MR:960541. Zbl:0652.60081.},
ISSN = {0075-8434},
ISBN = {9783540193517},
}
P. Biane, J. Pitman, and M. Yor :
“Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions ,”
Bull. Am. Math. Soc. (N.S.)
38 : 4
(2001 ),
pp. 435–465 .
MR
1848256
Zbl
1040.11061
ArXiv
math.PR/9912170
article
Abstract
People
BibTeX
This paper reviews known results which connect Riemann’s integral representations of his zeta function, involving Jacobi’s theta function and its derivatives, to some particular probability laws governing sums of independent exponential variables. These laws are related to one-dimensional Brownian motion and to higher dimensional Bessel processes. We present some characterizations of these probability laws, and some approximations of Riemann’s zeta function which are related to these laws.
@article {key1848256m,
AUTHOR = {Biane, Philippe and Pitman, Jim and
Yor, Marc},
TITLE = {Probability laws related to the {J}acobi
theta and {R}iemann zeta functions,
and {B}rownian excursions},
JOURNAL = {Bull. Am. Math. Soc. (N.S.)},
FJOURNAL = {American Mathematical Society. Bulletin.
New Series},
VOLUME = {38},
NUMBER = {4},
YEAR = {2001},
PAGES = {435--465},
DOI = {10.1090/S0273-0979-01-00912-0},
NOTE = {ArXiv:math.PR/9912170. MR:1848256.
Zbl:1040.11061.},
ISSN = {0273-0979},
}
J. Bertoin, P. Biane, and M. Yor :
“Poissonian exponential functionals, \( q \) -series, \( q \) -integrals, and the moment problem for log-normal distributions ,”
pp. 45–56
in
Seminar on stochastic analysis, random fields and applications IV
(Ascona, Switzerland, 20–24 May 2002 ).
Edited by R. C. Dalang, M. Dozzi, and F. Russo .
Progress in Probability 58 .
Birkhäuser (Basel ),
2004 .
MR
2096279
Zbl
1056.60046
incollection
Abstract
People
BibTeX
@incollection {key2096279m,
AUTHOR = {Bertoin, Jean and Biane, Philippe and
Yor, Marc},
TITLE = {Poissonian exponential functionals,
\$q\$-series, \$q\$-integrals, and the moment
problem for log-normal distributions},
BOOKTITLE = {Seminar on stochastic analysis, random
fields and applications {IV}},
EDITOR = {Dalang, Robert C. and Dozzi, Marco and
Russo, Francesco},
SERIES = {Progress in Probability},
NUMBER = {58},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Basel},
YEAR = {2004},
PAGES = {45--56},
DOI = {10.1007/978-3-0348-7943-9_3},
NOTE = {(Ascona, Switzerland, 20--24 May 2002).
MR:2096279. Zbl:1056.60046.},
ISSN = {1050-6977},
ISBN = {9783764371319},
}