J. Pitman and M. Yor :
“Decomposition at the maximum for excursions and bridges of one-dimensional diffusions 293–310
in
Itô’s stochastic calculus and probability theory .
Edited by N. Ikeda .
Springer (Tokyo ),
1996 .
Book dedicated to dedicated to Kiyosi Itô on the occasion of his 80th birthday.
MR
1439532 Zbl
0877.60053 incollection
Abstract
People
BibTeX
In his fundamental paper [1971], Itô showed how to construct a Poisson point process of excursions of a strong Markov process \( X \) over time intervals when \( X \) is away from a recurrent point a of its statespace. The point process is parameterized by the local time process of \( X \) at \( a \) . Each point of the excursion process is a path in a suitable space of possible excursions of \( X \) , starting at \( a \) at time 0, and returning to \( a \) for the first time at some strictly positive time \( \zeta \) , called the lifetime of the excursion. The intensity measure of the Poisson process of excursions is a \( \sigma \) -finite measure on the space of excursions, known as Itô’s excursion law. Accounts of Itô’s theory of excursions can now be found in several textbooks [Rogers and Williams 1987; Revuz and Yor 1994; Blumenthal 1992]. His theory has also been generalized to excursions of Markov processes away from a set of states [Maisonneuve 1975; Getoor and Sharpe 1982; Blumenthal 1992] and to excursions of stationary, not necessarily Markovian processes [Pitman 1986].
@incollection {key1439532m,
AUTHOR = {Pitman, Jim and Yor, Marc},
TITLE = {Decomposition at the maximum for excursions
and bridges of one-dimensional diffusions},
BOOKTITLE = {It\^o's stochastic calculus and probability
theory},
EDITOR = {Ikeda, Nobuyuki},
PUBLISHER = {Springer},
ADDRESS = {Tokyo},
YEAR = {1996},
PAGES = {293--310},
DOI = {10.1007/978-4-431-68532-6_19},
NOTE = {Book dedicated to dedicated to Kiyosi
It\^o on the occasion of his 80th birthday.
MR:1439532. Zbl:0877.60053.},
ISBN = {9784431701866},
}
M. Yor :
“How K. Itô revolutionized the study of stochastic processes Gaz. Math., Soc. Math. Fr.
111
(January 2007 ),
pp. 51–55 .
An English translation was published in Jpn. J. Math. 2 :1 (2007)
MR
2289679 Zbl
1149.60302 article
People
BibTeX
@article {key2289679m,
AUTHOR = {Yor, Marc},
TITLE = {How {K}. {I}t\^o revolutionized the
study of stochastic processes},
JOURNAL = {Gaz. Math., Soc. Math. Fr.},
FJOURNAL = {Gazette des Math\'ematiciens},
VOLUME = {111},
MONTH = {January},
YEAR = {2007},
PAGES = {51--55},
URL = {http://smf4.emath.fr/en/Publications/Gazette/2007/111/smf_gazette_111_51-55.pdf},
NOTE = {An English translation was published
in \textit{Jpn. J. Math.} \textbf{2}:1
(2007). MR:2289679. Zbl:1149.60302.},
ISSN = {0224-8999},
}
M. Yor :
“How K. Itô revolutionized the study of stochastic processes Jpn. J. Math. (3)
2 : 1
(March 2007 ),
pp. 137–143 .
English translation of French original published in Gaz. Math. 111 (2007)
MR
2295615 Zbl
1157.60325 article
Abstract
People
BibTeX
@article {key2295615m,
AUTHOR = {Yor, M.},
TITLE = {How {K}. {I}t\^o revolutionized the
study of stochastic processes},
JOURNAL = {Jpn. J. Math. (3)},
FJOURNAL = {Japanese Journal of Mathematics. 3rd
Series},
VOLUME = {2},
NUMBER = {1},
MONTH = {March},
YEAR = {2007},
PAGES = {137--143},
DOI = {10.1007/s11537-007-0713-4},
NOTE = {English translation of French original
published in \textit{Gaz. Math.} \textbf{111}
(2007). MR:2295615. Zbl:1157.60325.},
ISSN = {0289-2316},
}
M. Yor :
“Kiyosi Itô (1915–2008) Gaz. Math., Soc. Math. Fr.
119
(January 2009 ),
pp. 115 .
MR
2482837 article
People
BibTeX
@article {key2482837m,
AUTHOR = {Yor, Marc},
TITLE = {Kiyosi {I}t\^o (1915--2008)},
JOURNAL = {Gaz. Math., Soc. Math. Fr.},
FJOURNAL = {Gazette des Math\'ematiciens},
VOLUME = {119},
MONTH = {January},
YEAR = {2009},
PAGES = {115},
URL = {http://smf4.emath.fr/Publications/Gazette/2009/119/smf_gazette_119_115-115.pdf},
NOTE = {MR:2482837.},
ISSN = {0224-8999},
}
M. Yor and M. E. Vares :
“A tribute to Professor Kiyosi Itô Stochastic Process. Appl.
120 : 1
(January 2010 ),
pp. 104 .
This is a brief announcement of the special issue dedicated to Itô, Stochastic Process. Appl. 120 :5 (2010) .
MR
2565848 Zbl
1178.01066 article
People
BibTeX
@article {key2565848m,
AUTHOR = {Yor, M. and Vares, M. E.},
TITLE = {A tribute to {P}rofessor {K}iyosi {I}t\^o},
JOURNAL = {Stochastic Process. Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {120},
NUMBER = {1},
MONTH = {January},
YEAR = {2010},
PAGES = {104},
DOI = {10.1016/j.spa.2009.10.006},
NOTE = {This is a brief announcement of the
special issue dedicated to It\^o, \textit{Stochastic
Process. Appl.} \textbf{120}:5 (2010).
MR:2565848. Zbl:1178.01066.},
ISSN = {0304-4149},
}
M. Yor :
“Some aspects of K. Itô’s works Stochastic Process. Appl.
120 : 5
(May 2010 ),
pp. 577–579 .
Reprinted from Eur. Math. Soc. Newsl. 72 (2009)
MR
2603052 Zbl
1194.60002 article
People
BibTeX
@article {key2603052m,
AUTHOR = {Yor, Marc},
TITLE = {Some aspects of {K}. {I}t\^o's works},
JOURNAL = {Stochastic Process. Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {120},
NUMBER = {5},
MONTH = {May},
YEAR = {2010},
PAGES = {577--579},
DOI = {10.1016/j.spa.2010.01.007},
NOTE = {Reprinted from \textit{Eur. Math. Soc.
Newsl.} \textbf{72} (2009). MR:2603052.
Zbl:1194.60002.},
ISSN = {1027-488X},
}
F. Hirsch, B. Roynette, and M. Yor :
“Applying Itô’s motto: ‘Look at the infinite dimensional picture’ by constructing sheets to obtain processes increasing in the convex order Period. Math. Hung.
61 : 1–2
(2010 ),
pp. 195–211 .
MR
2728438 Zbl
1274.60052 article
Abstract
People
BibTeX
Strongly inspired by the result due to Carr–Ewald–Xiao that the arithmetic average of geometric Brownian motion is an increasing process in the convex order, we extend this result to integrals of Lévy processes and Gaussian processes. Our method consists in finding an appropriate sheet associated to the original Lévy or Gaussian process, from which the one-dimensional marginals of the integrals will appear to be those of a martingale, thus proving the increase in the convex order property.
@article {key2728438m,
AUTHOR = {Hirsch, Francis and Roynette, Bernard
and Yor, Marc},
TITLE = {Applying {I}t\^o's motto: ``{L}ook at
the infinite dimensional picture'' by
constructing sheets to obtain processes
increasing in the convex order},
JOURNAL = {Period. Math. Hung.},
FJOURNAL = {Periodica Mathematica Hungarica},
VOLUME = {61},
NUMBER = {1--2},
YEAR = {2010},
PAGES = {195--211},
DOI = {10.1007/s10998-010-3195-8},
NOTE = {MR:2728438. Zbl:1274.60052.},
ISSN = {0031-5303},
}
A tribute to Kiyosi Itô ,
published as Stochastic Process. Appl.
120 : 5 .
Issue edited by M. Yor and M. E. Vares .
Elsevier (Amsterdam ),
May 2010 .
A brief announcement of this special issue was published in Stochastic Process. Appl. 120 :1 (2010)
book
People
BibTeX
@book {key82269559,
TITLE = {A tribute to {K}iyosi {I}t\^o},
EDITOR = {Yor, M. and Vares, M. E.},
PUBLISHER = {Elsevier},
ADDRESS = {Amsterdam},
MONTH = {May},
YEAR = {2010},
PAGES = {575--766},
NOTE = {Published as \textit{Stochastic Process.
Appl.} \textbf{120}:5. A brief announcement
of this special issue was published
in \textit{Stochastic Process. Appl.}
\textbf{120}:1 (2010).},
ISSN = {0304-4149},
}
M. Yor and M. E. Vares :
“Introducing the volume 585–589
in
A tribute to Kiyosi Itô ,
published as Stochastic Processes Appl.
120 : 5 (special issue) .
Issue edited by M. Yor and M. E. Vares .
Elsevier (Amsterdam ),
May 2010 .
Zbl
1203.60003 incollection
People
BibTeX
@article {key1203.60003z,
AUTHOR = {Yor, Marc and Vares, Maria Eul\'alia},
TITLE = {Introducing the volume},
JOURNAL = {Stochastic Processes Appl.},
FJOURNAL = {Stochastic Processes and their Applications},
VOLUME = {120},
NUMBER = {5 (special issue)},
MONTH = {May},
YEAR = {2010},
PAGES = {585--589},
DOI = {10.1016/j.spa.2010.01.011},
NOTE = {\textit{A tribute to {K}iyosi {I}t\^o}.
Issue edited by M. Yor and M. E. Vares.
Zbl:1203.60003.},
ISSN = {0304-4149},
}
