M. Yor :
“Some remarkable properties of gamma processes ,”
pp. 37–47
in
Advances in mathematical finance
(College Park, MD, 29 September–1 October 1 2006 ).
Edited by M. C. Fu, R. A. Jarrow, J.-Y. Yen, and R. J. Elliott .
Applied Numerical Harmonic Analysis .
Birkhäuser (Boston, MA ),
2007 .
Paper presented at the mathematical finance conference in honor of the 60th birthday of Dilip B. Madan.
MR
2359361
Zbl
1156.60030
incollection
Abstract
People
BibTeX
A number of remarkable properties of gamma processes are gathered in this paper, including realisation of their bridges, absolute continuity relationships, realisation of a gamma process as an inverse local time, and the effect of a gamma process as a time change. Some of them are put in perspective with their Brownian counterparts.
@incollection {key2359361m,
AUTHOR = {Yor, Marc},
TITLE = {Some remarkable properties of gamma
processes},
BOOKTITLE = {Advances in mathematical finance},
EDITOR = {Fu, Michael C. and Jarrow, Robert A.
and Yen, Ju-Yi and Elliott, Robert J.},
SERIES = {Applied Numerical Harmonic Analysis},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston, MA},
YEAR = {2007},
PAGES = {37--47},
DOI = {10.1007/978-0-8176-4545-8_3},
NOTE = {(College Park, MD, 29 September--1 October
1 2006). Paper presented at the mathematical
finance conference in honor of the 60th
birthday of Dilip B. Madan. MR:2359361.
Zbl:1156.60030.},
ISSN = {2296-5009},
ISBN = {9780817645441},
}
M. Yor :
“A note about Selberg’s integrals in relation with the beta-gamma algebra ,”
pp. 49–58
in
Advances in mathematical finance
(College Park, MD, 29 September–1 October 1 2006 ).
Edited by M. C. Fu, R. A. Jarrow, J.-Y. Yen, and R. J. Elliott .
Applied Numerical Harmonic Analysis .
Birkhäuser (Boston, MA ),
2007 .
Paper presented at the mathematical finance conference in honor of the 60th birthday of Dilip B. Madan.
MR
2359362
Zbl
1160.33002
incollection
Abstract
People
BibTeX
To prove their formulae for the moments of the characteristic polynomial of the generic matrix of \( U(N) \) , Keating and Snaith [2000] (see also Keating [2004]) use Selberg’s integrals as a ‘black box’. In this note, we point out some identities in law which are equivalent to the expressions of Selberg’s integrals and which involve beta, gamma, and normal variables. However, this is a mere probabilistic translation of Selberg’s results, and does not provide an independent proof of them. An outcome of some of these translations is that certain logarithms of (Vandermonde) random discriminants are self-decomposable, which hinges on the self-decomposability of the logarithms of the beta \( (a,b) \) (\( 2a + b \geq 1 \) ) and gamma (\( a \gt 0 \) ) variables. Such selfdecomposability properties have been of interest in some joint papers with D. Madan.
@incollection {key2359362m,
AUTHOR = {Yor, Marc},
TITLE = {A note about {S}elberg's integrals in
relation with the beta-gamma algebra},
BOOKTITLE = {Advances in mathematical finance},
EDITOR = {Fu, Michael C. and Jarrow, Robert A.
and Yen, Ju-Yi and Elliott, Robert J.},
SERIES = {Applied Numerical Harmonic Analysis},
PUBLISHER = {Birkh\"auser},
ADDRESS = {Boston, MA},
YEAR = {2007},
PAGES = {49--58},
DOI = {10.1007/978-0-8176-4545-8_4},
NOTE = {(College Park, MD, 29 September--1 October
1 2006). Paper presented at the mathematical
finance conference in honor of the 60th
birthday of Dilip B. Madan. MR:2359362.
Zbl:1160.33002.},
ISSN = {2296-5009},
ISBN = {9780817645441},
}
J. Yen and M. Yor :
Moments thoughts about an integration by parts in distribution for Brownian quadratic functionals ,
2010 .
unpublished
People
BibTeX
@unpublished {key84201481,
AUTHOR = {Yen, J.Y. and Yor, Marc},
TITLE = {Moments thoughts about an integration
by parts in distribution for {B}rownian
quadratic functionals},
YEAR = {2010},
}
J.-Y. Yen and M. Yor :
“Truncation functions and Laplace transform ,”
Stat. Probab. Lett.
81 : 3
(March 2011 ),
pp. 417–419 .
MR
2748950
Zbl
1209.60012
article
Abstract
People
BibTeX
@article {key2748950m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {Truncation functions and {L}aplace transform},
JOURNAL = {Stat. Probab. Lett.},
FJOURNAL = {Statistics \& Probability Letters},
VOLUME = {81},
NUMBER = {3},
MONTH = {March},
YEAR = {2011},
PAGES = {417--419},
DOI = {10.1016/j.spl.2010.12.006},
NOTE = {MR:2748950. Zbl:1209.60012.},
ISSN = {0167-7152},
}
J.-Y. Yen and M. Yor :
“Call option prices based on Bessel processes ,”
Methodol. Comput. Appl. Probab.
13 : 2
(June 2011 ),
pp. 329–347 .
MR
2788861
Zbl
1217.60071
ArXiv
0808.3402
article
Abstract
People
BibTeX
As a complement to some recent work by Pal and Protter [2007, 2009], we show that the call option prices associated with the Bessel strict local martingales are integrable over time, and we discuss the probability densities obtained thus.
@article {key2788861m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {Call option prices based on {B}essel
processes},
JOURNAL = {Methodol. Comput. Appl. Probab.},
FJOURNAL = {Methodology and Computing in Applied
Probability},
VOLUME = {13},
NUMBER = {2},
MONTH = {June},
YEAR = {2011},
PAGES = {329--347},
DOI = {10.1007/s11009-009-9151-5},
NOTE = {ArXiv:0808.3402. MR:2788861. Zbl:1217.60071.},
ISSN = {1387-5841},
}
C.-T. Wu, J.-Y. Yen, and M. Yor :
“Measuring the ‘non-stopping timeness’ of ends of previsible sets ,”
Taiwanese J. Math.
16 : 5
(October 2012 ),
pp. 1589–1599 .
MR
2970673
Zbl
1273.60049
ArXiv
0810.1059
article
Abstract
People
BibTeX
In this paper, we propose several “measurements” of the “non-stopping timeness” of ends \( \mathcal{G} \) of previsible sets, such that \( \mathcal{G} \) avoids stopping times, in an ambiant filtration. We then study several explicit examples, involving last passage times of some remarkable martingales.
@article {key2970673m,
AUTHOR = {Wu, Ching-Tang and Yen, Ju-Yi and Yor,
Marc},
TITLE = {Measuring the ``non-stopping timeness''
of ends of previsible sets},
JOURNAL = {Taiwanese J. Math.},
FJOURNAL = {Taiwanese Journal of Mathematics},
VOLUME = {16},
NUMBER = {5},
MONTH = {October},
YEAR = {2012},
PAGES = {1589--1599},
DOI = {10.11650/twjm/1500406785},
NOTE = {ArXiv:0810.1059. MR:2970673. Zbl:1273.60049.},
ISSN = {1027-5487},
}
A. P. C. Lim, J.-Y. Yen, and M. Yor :
“Some examples of Skorokhod embeddings obtained from the Azéma–Yor algorithm ,”
Stochastic Process. Appl.
123 : 2
(February 2013 ),
pp. 329–346 .
MR
3003354
Zbl
1258.60032
article
Abstract
People
BibTeX
As discussed in Madan and Yor [2002], under certain conditions on a family \( (H_r \) , \( r\gt 0) \) of Hardy–Littlewood functions, Markovian martingales \( (B_{T_{H_r}}) \) may be constructed. We take advantage of the explicit character of the Azéma–Yor (Skorokhod embedding) algorithm, to describe precisely some remarkable and simple examples of these Markovian martingales.
@article {key3003354m,
AUTHOR = {Lim, Adrian P. C. and Yen, Ju-Yi and
Yor, Marc},
TITLE = {Some examples of {S}korokhod embeddings
obtained from the {A}z\'ema--{Y}or algorithm},
JOURNAL = {Stochastic Process. Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {123},
NUMBER = {2},
MONTH = {February},
YEAR = {2013},
PAGES = {329--346},
DOI = {10.1016/j.spa.2012.09.013},
NOTE = {MR:3003354. Zbl:1258.60032.},
ISSN = {0304-4149},
}
J.-Y. Yen and M. Yor :
“Illustration of various methods for solving partly Skorokhod’s embedding problem ,”
Electron. Commun. Probab.
18 : 48
(2013 ).
Article no. 48, 5 pp.
MR
3078011
Zbl
1326.60056
article
Abstract
People
BibTeX
@article {key3078011m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {Illustration of various methods for
solving partly {S}korokhod's embedding
problem},
JOURNAL = {Electron. Commun. Probab.},
FJOURNAL = {Electronic Communications in Probability},
VOLUME = {18},
NUMBER = {48},
YEAR = {2013},
DOI = {10.1214/ECP.v18-2178},
NOTE = {Article no. 48, 5 pp. MR:3078011. Zbl:1326.60056.},
ISSN = {1083-589X},
}
J.-Y. Yen and M. Yor :
“On an identity in law between Brownian quadratic functionals ,”
Statist. Probab. Lett.
83 : 9
(September 2013 ),
pp. 2015–2018 .
MR
3079037
Zbl
1290.60081
article
Abstract
People
BibTeX
@article {key3079037m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {On an identity in law between {B}rownian
quadratic functionals},
JOURNAL = {Statist. Probab. Lett.},
FJOURNAL = {Statistics \& Probability Letters},
VOLUME = {83},
NUMBER = {9},
MONTH = {September},
YEAR = {2013},
PAGES = {2015--2018},
DOI = {10.1016/j.spl.2013.05.013},
NOTE = {MR:3079037. Zbl:1290.60081.},
ISSN = {0167-7152},
}
J.-Y. Yen and M. Yor :
Local times and excursion theory for Brownian motion: A tale of Wiener and Itô measures .
Lecture Notes in Mathematics 2088 .
Springer (Cham, Switzerland ),
2013 .
MR
3134857
Zbl
1364.60003
book
People
BibTeX
@book {key3134857m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {Local times and excursion theory for
Brownian motion: {A} tale of {W}iener
and {I}t\^o measures},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {2088},
PUBLISHER = {Springer},
ADDRESS = {Cham, Switzerland},
YEAR = {2013},
PAGES = {x+135},
DOI = {10.1007/978-3-319-01270-4},
NOTE = {MR:3134857. Zbl:1364.60003.},
ISSN = {0075-8434},
ISBN = {9783319012698},
}
J.-Y. Yen and M. Yor :
(Planar) Brownian motion as a key stochastic process ,
2013 .
Conference paper delivered at the seminar “Ars Conjectandi: A celebration of 300 years of stochastics,” Freiburg-Basel, Germany, 21–24 May 2013.
unpublished
People
BibTeX
@unpublished {key73145605,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {(Planar) {B}rownian motion as a key
stochastic process},
YEAR = {2013},
NOTE = {Conference paper delivered at the seminar
``Ars Conjectandi: A celebration of
300 years of stochastics'', Freiburg-Basel,
Germany, 21--24 May 2013.},
}
J.-Y. Yen and M. Yor :
“A variant of Pitman’s theorem on \( (2J_s-R_s \) , \( s\geq 0) \) for a general transient Bessel process \( R_{(+)} \) and its implications for the corresponding Ito’s measure \( \mathbf{n}_{(-)} \) ,”
J. Theor. Probab.
28 : 1
(March 2015 ),
pp. 223–230 .
MR
3320966
Zbl
1327.60160
article
Abstract
People
BibTeX
Projection properties of the future infimum of a transient Bessel process \( R_{(+)} \) with dimension \( d_{(+)} = 2(1+ \alpha) \) (\( \alpha \in (0,1) \) ) as well as the definition of the local time \( (L_t) \) of a recurrent Bessel process \( R_{(+)} \) with dimension \( d_{(+)} = 2(1 - \alpha) \) as the compensator of \( (R_{(+)})^{2 \alpha} \) may be seen to play some hidden but quite efficient role to obtain several integral representation formulae for the excursion theory of the \( R_{(+)} \) process away from 0. The precise formulae, which involve simple universal constants, are quite useful when dealing with the whole family of Bessel processes for dimensions between 0 and 2 (i.e., the reflecting case) and between 2 and 4 (i.e., the transient case).
@article {key3320966m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {A variant of {P}itman's theorem on \$(2J_s-R_s\$,
\$s\geq 0)\$ for a general transient {B}essel
process \$R_{(+)}\$ and its implications
for the corresponding {I}to's measure
\$\mathbf{n}_{(-)}\$},
JOURNAL = {J. Theor. Probab.},
FJOURNAL = {Journal of Theoretical Probability},
VOLUME = {28},
NUMBER = {1},
MONTH = {March},
YEAR = {2015},
PAGES = {223--230},
DOI = {10.1007/s10959-013-0505-0},
NOTE = {MR:3320966. Zbl:1327.60160.},
ISSN = {0894-9840},
}
J.-Y. Yen and M. Yor :
“On two results of P. Deheuvels ,”
pp. 305–308
in
Mathematical statistics and limit theorems: Festschrift in honour of Paul Deheuvels
(Paris, 20–21 June 2013 ).
Edited by M. Hallin, D. Mason, D. Pfeifer, and J. Steinebach .
Springer (Cham, Switzerland ),
2015 .
MR
3380743
Zbl
1317.60108
incollection
Abstract
People
BibTeX
@incollection {key3380743m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {On two results of {P}. {D}eheuvels},
BOOKTITLE = {Mathematical statistics and limit theorems:
{F}estschrift in honour of {P}aul {D}eheuvels},
EDITOR = {Hallin, Marc and Mason, David and Pfeifer,
Dietmar and Steinebach, Josef},
PUBLISHER = {Springer},
ADDRESS = {Cham, Switzerland},
YEAR = {2015},
PAGES = {305--308},
NOTE = {(Paris, 20--21 June 2013). MR:3380743.
Zbl:1317.60108.},
ISBN = {9783319124414},
}
J.-Y. Yen and M. Yor :
“Some topics in probability theory ,”
pp. 309–314
in
Mathematical statistics and limit theorems: Festschrift in honour of Paul Deheuvels
(Paris, 20–21 June 2013 ).
Edited by M. Hallin, D. Mason, D. Pfeifer, and J. G. Steinebach .
Springer (Cham, Switzerland ),
2015 .
MR
3380744
Zbl
1328.60002
incollection
Abstract
People
BibTeX
@incollection {key3380744m,
AUTHOR = {Yen, Ju-Yi and Yor, Marc},
TITLE = {Some topics in probability theory},
BOOKTITLE = {Mathematical statistics and limit theorems:
{F}estschrift in honour of {P}aul {D}eheuvels},
EDITOR = {Hallin, Marc and Mason, David and Pfeifer,
Dietmar and Steinebach, Josef G.},
PUBLISHER = {Springer},
ADDRESS = {Cham, Switzerland},
YEAR = {2015},
PAGES = {309--314},
DOI = {10.1007/978-3-319-12442-1_18},
NOTE = {(Paris, 20--21 June 2013). MR:3380744.
Zbl:1328.60002.},
ISBN = {9783319124414},
}
P. Salminen, J.-Y. Yen, and M. Yor :
“Integral representations of certain measures in the one-dimensional diffusions excursion theory ,”
pp. 1–15
in
In memoriam Marc Yor: Séminaire de probabilités XLVII
[In memoriam Marc Yor: Forty-seventh probability seminar ].
Edited by C. Donati-Martin, A. Lejay, and A. Rouault .
Lecture Notes in Mathematics 2137 .
Springer (Cham, Switzerland ),
2015 .
MR
3444291
Zbl
1334.60165
incollection
Abstract
People
BibTeX
In this note we present integral representations of the Itô excursion measure associated with a general one-dimensional diffusion \( X \) . These representations and identities are natural extensions of the classical ones for reflected Brownian motion, RBM. As is well known, the three-dimensional Bessel process, \( \mathrm{BES}(3) \) , plays a crucial rôle in the analysis of the Brownian excursions. Our main interest is in showing explicitly how certain excursion theoretical formulae associated with the pair \( (\mathrm{RBM} \) , \( \mathrm{BES}(3)) \) generalize to pair \( (X,X^{\uparrow}) \) , where \( X^{\uparrow} \) denotes the diffusion obtained from \( X \) by conditioning \( X \) not to hit 0. We illustrate the results for the pair \( (R_-,R_+) \) consisting of a recurrent Bessel process with dimension \( d_- = 2(1-\alpha) \) , \( \alpha\in (0,1) \) , and a transient Bessel process with dimension \( d_+ = 2(1 + \alpha) \) . Pair \( (\mathrm{RBM} \) , \( \mathrm{BES}(3)) \) is, clearly, obtained by choosing \( \alpha=1/2 \) .
@incollection {key3444291m,
AUTHOR = {Salminen, Paavo and Yen, Ju-Yi and Yor,
Marc},
TITLE = {Integral representations of certain
measures in the one-dimensional diffusions
excursion theory},
BOOKTITLE = {In memoriam {M}arc {Y}or: {S}\'eminaire
de probabilit\'es {XLVII} [In memoriam
{M}arc {Y}or: {F}orty-seventh probability
seminar]},
EDITOR = {Donati-Martin, Catherine and Lejay,
Antoine and Rouault, Alain},
SERIES = {Lecture Notes in Mathematics},
NUMBER = {2137},
PUBLISHER = {Springer},
ADDRESS = {Cham, Switzerland},
YEAR = {2015},
PAGES = {1--15},
DOI = {10.1007/978-3-319-18585-9_1},
NOTE = {MR:3444291. Zbl:1334.60165.},
ISSN = {0075-8434},
ISBN = {9783319185842},
}