@incollection {azencott-82,
AUTHOR = {Azencott, Robert},
TITLE = {Formule de {T}aylor stochastique et d\'eveloppement
asymptotique d'int\'egrales de {F}eynman},
BOOKTITLE = {Seminar on Probability, XVI, Supplement},
PAGES = {237--285},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1982},
MRCLASS = {60H10 (58C20 58G32 60J60 81C35)},
MRNUMBER = {84a:60065}
}
@unpublished{bass-hambly-lyons-01,
author = {Bass, R. F. and Hambly, Ben and Lyons, Terry},
title = {Extending the {W}ong-{Z}akai theorem to reversible {M}arkov
processes},
note = {preprint, to appear in J. Eur. Math. Soc.},
year = {2001}
}
@article {benarous-89,
AUTHOR = {Ben Arous, G{\'e}rard},
TITLE = {Flots et s\'eries de {T}aylor stochastiques},
JOURNAL = {Probab. Theory Related Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {81},
YEAR = {1989},
NUMBER = {1},
PAGES = {29--77},
ISSN = {0178-8051},
CODEN = {PTRFEU},
MRCLASS = {60H10 (58G32)},
MRNUMBER = {90a:60106}
}
@book {bouleau-lepingle-94,
AUTHOR = {Bouleau, Nicolas and L{\'e}pingle, Dominique},
TITLE = {Numerical methods for stochastic processes},
NOTE = {A Wiley-Interscience Publication},
PUBLISHER = {John Wiley \& Sons Inc.},
ADDRESS = {New York},
YEAR = {1994},
PAGES = {xx+359},
ISBN = {0-471-54641-0},
MRCLASS = {60H10 (60-04 60J99 65U05)},
MRNUMBER = {95h:60090}
}
@book {bourbaki-72,
AUTHOR = {Bourbaki, N.},
TITLE = {\'{E}l\'ements de math\'ematique. {F}asc.
{X}{X}{X}{V}{I}{I}. {G}roupes et alg\`ebres de {L}ie.
{C}hapitre {I}{I}: {A}lg\`ebres de {L}ie libres. {C}hapitre
{I}{I}{I}: {G}roupes de {L}ie},
NOTE = {Actualit\'es Scientifiques et Industrielles, No. 1349},
PUBLISHER = {Hermann},
ADDRESS = {Paris},
YEAR = {1972},
PAGES = {320},
MRCLASS = {17-01 (22-01)},
MRNUMBER = {58 \#28083a}
}
@article {burrage-burrage-00,
AUTHOR = {Burrage, K. and Burrage, P. M.},
TITLE = {Order conditions of stochastic {R}unge-{K}utta methods by
{$B$}-series},
JOURNAL = {SIAM J. Numer. Anal.},
FJOURNAL = {SIAM Journal on Numerical Analysis},
VOLUME = {38},
YEAR = {2000},
NUMBER = {5},
PAGES = {1626--1646 (electronic)},
ISSN = {1095-7170},
MRCLASS = {65C30 (65L06)},
MRNUMBER = {2001m:65016},
MRREVIEWER = {Alexander Ostermann},
}
@article {capitaine-01,
AUTHOR = {Capitaine, Mireille and Donati-Martin, Catherine},
TITLE = {The {L}\'evy area process for the free {B}rownian motion},
JOURNAL = {J. Funct. Anal.},
FJOURNAL = {Journal of Functional Analysis},
VOLUME = {179},
YEAR = {2001},
NUMBER = {1},
PAGES = {153--169},
ISSN = {0022-1236},
CODEN = {JFUAAW},
MRCLASS = {46L54 (60J65)},
MRNUMBER = {2001k:46103}
}
@article {castell,
AUTHOR = {Castell, Fabienne},
TITLE = {Asymptotic expansion of stochastic flows},
JOURNAL = {Probab. Theory Related Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {96},
YEAR = {1993},
NUMBER = {2},
PAGES = {225--239},
ISSN = {0178-8051},
CODEN = {PTRFEU},
MRCLASS = {60H10},
MRNUMBER = {94g:60110},
MRREVIEWER = {Daniel Ocone},
}
@article {castell-gaines-95,
AUTHOR = {Castell, Fabienne and Gaines, Jessica},
TITLE = {An efficient approximation method for stochastic
differential equations by means of the exponential {L}ie
series},
NOTE = {Probabilit\'es num\'eriques (Paris, 1992)},
JOURNAL = {Math. Comput. Simulation},
FJOURNAL = {Mathematics and Computers in Simulation},
VOLUME = {38},
YEAR = {1995},
NUMBER = {1-3},
PAGES = {13--19},
ISSN = {0378-4754},
CODEN = {MCSIDR},
MRCLASS = {60H10 (65U05)},
MRNUMBER = {96e:60101}
}
@article {castell-gaines-96,
AUTHOR = {Castell, Fabienne and Gaines, Jessica},
TITLE = {The ordinary differential equation approach to
asymptotically efficient schemes for solution of stochastic
differential equations},
JOURNAL = {Ann. Inst. H. Poincar\'e Probab. Statist.},
FJOURNAL = {Annales de l'Institut Henri Poincar\'e. Probabilit\'es et
Statistiques},
VOLUME = {32},
YEAR = {1996},
NUMBER = {2},
PAGES = {231--250},
ISSN = {0246-0203},
CODEN = {AHPBAR},
MRCLASS = {60H10 (65L99 65U05)},
MRNUMBER = {97c:60148}
}
@article {chen-57,
AUTHOR = {Chen, Kuo-Tsai},
TITLE = {Integration of paths, geometric invariants and a generalized
{B}aker-{H}ausdorff formula},
JOURNAL = {Ann. of Math. (2)},
VOLUME = {65},
YEAR = {1957},
PAGES = {163--178},
MRCLASS = {20.0X},
MRNUMBER = {19,12a}
}
@article {chen-58,
AUTHOR = {Chen, Kuo-Tsai},
TITLE = {Integration of paths---a faithful representation of paths by
non-commutative formal power series},
JOURNAL = {Trans. Amer. Math. Soc.},
VOLUME = {89},
YEAR = {1958},
PAGES = {395--407},
MRCLASS = {22.00},
MRNUMBER = {21 \#4992}
}
@article {chistyakov-galkin-98,
AUTHOR = {Chistyakov, V. V. and Galkin, O. E.},
TITLE = {On maps of bounded $p$-variation with $p>1$},
JOURNAL = {Positivity},
FJOURNAL = {Positivity. An International Journal devoted to the Theory
and Applications of Positivity in Analysis},
VOLUME = {2},
YEAR = {1998},
NUMBER = {1},
PAGES = {19--45},
ISSN = {1385-1292},
CODEN = {PSITFL},
MRCLASS = {26A45 (26A16 26E25 49J45)},
MRNUMBER = {2000h:26016}
}
@article {coutin-qian-00,
AUTHOR = {Coutin, Laure and Qian, Zhongmin},
TITLE = {Stochastic differential equations for fractional {B}rownian
motions},
JOURNAL = {C. R. Acad. Sci. Paris S\'er. I Math.},
FJOURNAL = {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
Math\'ematique},
VOLUME = {331},
YEAR = {2000},
NUMBER = {1},
PAGES = {75--80},
ISSN = {0764-4442},
CODEN = {CASMEI},
MRCLASS = {60G18 (60H10)},
MRNUMBER = {2001d:60038}
}
@article {coutin-qian-02,
AUTHOR = {Coutin, Laure and Qian, Zhongmin},
TITLE = {Stochastic analysis, rough path analysis and fractional
{B}rownian motions},
JOURNAL = {Probab. Theory Related Fields},
FJOURNAL = {Probability Theory and Related Fields},
VOLUME = {122},
YEAR = {2002},
NUMBER = {1},
PAGES = {108--140},
ISSN = {0178-8051},
CODEN = {PTRFEU},
MRCLASS = {60D05 (60G15 60H07)},
MRNUMBER = {1 883 719}
}
@article {doss-76,
AUTHOR = {Doss, Halim},
TITLE = {Liens entre \'equations diff\'erentielles stochastiques et
ordinaires},
JOURNAL = {C. R. Acad. Sci. Paris S\'er. A-B},
VOLUME = {283},
YEAR = {1976},
NUMBER = {13},
PAGES = {Ai, A939--A942},
MRCLASS = {60H10 (34F05)},
MRNUMBER = {54 \#14098}
}
@article {doss-77,
AUTHOR = {Doss, Halim},
TITLE = {Liens entre \'equations diff\'erentielles stochastiques et
ordinaires},
JOURNAL = {Ann. Inst. H. Poincar\'e Sect. B (N.S.)},
VOLUME = {13},
YEAR = {1977},
NUMBER = {2},
PAGES = {99--125},
MRCLASS = {60H10 (34F05)},
MRNUMBER = {56 \#9690}
}
@unpublished{dudley-norvaisa-98,
author = {Dudley, R.M. and Norvai{\v s}a, R.},
title = {An introduction to $p$-variation and {Y}oung integrals --
with emphasis on sample functions of stochastic processes},
note = {Lecture given at the {C}entre for {M}athematical {P}hysics
and {S}tochastics, {D}epartment of {M}athematical
{S}ciences, {U}niversity of Aarhus},
year = {1998}
}
@book {dudley-norvaisa-99,
AUTHOR = {Dudley, Richard M. and Norvai{\v{s}}a, Rimas},
TITLE = {Differentiability of six operators on nonsmooth functions
and {$p$}-variation},
SERIES = {Lecture Notes in Mathematics},
VOLUME = {1703},
NOTE = {With the collaboration of Jinghua Qian},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1999},
PAGES = {viii+277},
ISBN = {3-540-65975-7},
MRCLASS = {46G05 (26A45 26E15 47H30 58C20)},
MRNUMBER = {2000e:46053},
MRREVIEWER = {Vladimir I. Bogachev},
}
@incollection {follmer-81,
AUTHOR = {F{\"o}llmer, H.},
TITLE = {Calcul d'{I}t\^o sans probabilit\'es},
BOOKTITLE = {Seminar on Probability, XV (Univ. Strasbourg, Strasbourg,
1979/1980) (French)},
PAGES = {143--150},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1981},
MRCLASS = {60H05},
MRNUMBER = {82j:60098}
}
@article {gaines-lyons-94,
AUTHOR = {Gaines, J. G. and Lyons, Terry},
TITLE = {Random generation of stochastic area integrals},
JOURNAL = {SIAM J. Appl. Math.},
FJOURNAL = {SIAM Journal on Applied Mathematics},
VOLUME = {54},
YEAR = {1994},
NUMBER = {4},
PAGES = {1132--1146},
ISSN = {0036-1399},
CODEN = {SMJMAP},
MRCLASS = {60H10 (93E30)},
MRNUMBER = {95f:60063}
}
@article {gaines-lyons-97,
AUTHOR = {Gaines, J. G. and Lyons, Terry},
TITLE = {Variable step size control in the numerical solution of
stochastic differential equations},
JOURNAL = {SIAM J. Appl. Math.},
FJOURNAL = {SIAM Journal on Applied Mathematics},
VOLUME = {57},
YEAR = {1997},
NUMBER = {5},
PAGES = {1455--1484},
ISSN = {0036-1399},
CODEN = {SMJMAP},
MRCLASS = {60H10 (65C20 65U05)},
MRNUMBER = {98m:60089}
}
@unpublished {hambly-lyons-02,
AUTHOR = {Hambly, Ben and Lyons, Terry},
TITLE = {Uniqueness for the {S}ignature of a {P}ath of {B}ounded
{V}ariation},
YEAR = {2002},
NOTE = {Preprint}
}
@article {hambly-lyons-98,
AUTHOR = {Hambly, Ben and Lyons, Terry},
TITLE = {Stochastic area for {B}rownian motion on the {S}ierpinski
gasket},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {26},
YEAR = {1998},
NUMBER = {1},
PAGES = {132--148},
ISSN = {0091-1798},
CODEN = {APBYAE},
MRCLASS = {60J65 (60H10)},
MRNUMBER = {99f:60145}
}
@incollection {hu,
AUTHOR = {Hu, Yao Zhong},
TITLE = {S\'erie de {T}aylor stochastique et formule de
{C}ampbell-{H}ausdorff, d'apr\`es {B}en {A}rous},
BOOKTITLE = {S\'eminaire de Probabilit\'es, XXVI},
SERIES = {Lecture Notes in Math.},
VOLUME = {1526},
PAGES = {579--586},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1992},
MRCLASS = {60H10},
MRNUMBER = {94j:60117},
MRREVIEWER = {Fabienne Castell}
}
@book {ikeda-watanabe-81,
AUTHOR = {Ikeda, Nobuyuki and Watanabe, Shinzo},
TITLE = {Stochastic differential equations and diffusion processes},
PUBLISHER = {North-Holland Publishing Co.},
ADDRESS = {Amsterdam},
YEAR = {1981},
PAGES = {xiv+464},
ISBN = {0-444-86172-6},
MRCLASS = {60H10 (34F05 58G32 60J60)},
MRNUMBER = {84b:60080}
}
@book {ikeda-watanabe-89,
AUTHOR = {Ikeda, Nobuyuki and Watanabe, Shinzo},
TITLE = {Stochastic differential equations and diffusion processes},
EDITION = {Second},
PUBLISHER = {North-Holland Publishing Co.},
ADDRESS = {Amsterdam},
YEAR = {1989},
PAGES = {xvi+555},
ISBN = {0-444-87378-3},
MRCLASS = {60H10 (58G32 60J60)},
MRNUMBER = {90m:60069}
}
@book {kloeden-platen-92,
AUTHOR = {Kloeden, Peter and Platen, Eckhard},
TITLE = {Numerical solution of stochastic differential equations},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1992},
PAGES = {xxxvi+632},
ISBN = {3-540-54062-8},
MRCLASS = {60H10 (34A50 34F05 65L99 65P05)},
MRNUMBER = {94b:60069}
}
@book {kloeden-platen-schurz-94,
AUTHOR = {Kloeden, Peter and Platen, Eckhard and Schurz, Henri},
TITLE = {Numerical solution of {S}{D}{E} through computer
experiments},
NOTE = {With 1 IBM-PC floppy disk (3.5 inch; HD)},
PUBLISHER = {Springer-Verlag},
ADDRESS = {Berlin},
YEAR = {1994},
PAGES = {xiv+292},
ISBN = {3-540-57074-8},
MRCLASS = {60H10 (34-04 34F05 65U05)},
MRNUMBER = {95a:60084}
}
@incollection {kunita-80,
AUTHOR = {Kunita, Hiroshi},
TITLE = {On the representation of solutions of stochastic
differential equations},
BOOKTITLE = {Seminar on Probability, XIV (Paris, 1978/1979) (French)},
PAGES = {282--304},
PUBLISHER = {Springer},
ADDRESS = {Berlin},
YEAR = {1980},
MRCLASS = {58D25 (58G32 60H10)},
MRNUMBER = {82e:58028}
}
@article {ledoux-lyons-qian-02,
AUTHOR = {Ledoux, Michel and Lyons, Terry and Qian, Zhongmin},
TITLE = {L\'evy area of {W}iener processes in {B}anach spaces},
JOURNAL = {Ann. Probab.},
FJOURNAL = {The Annals of Probability},
VOLUME = {30},
YEAR = {2002},
NUMBER = {2},
PAGES = {546--578},
ISSN = {0091-1798},
CODEN = {APBYAE},
MRCLASS = {60H10 (60G15 60H15 60J60)},
MRNUMBER = {1 905 851}
}
@unpublished{ledoux-qian-zhang-02,
AUTHOR = {Ledoux, Michel and Qian, Zhongmin and Zhang, T.},
TITLE = {Large deviations and support theorem for diffusion processes
via rough paths},
YEAR = {2002},
NOTE = {To appear in Stoch. Proc. Appl.}
}
@unpublished{lejay-02,
AUTHOR = {Lejay, Antoine},
TITLE = {Stochastic differential equations driven by a processes
generated by divergence form operators},
NOTE = {preprint, \url{http://www.iecn.u-nancy.fr/~lejay/rough.html}},
YEAR = {2002}
}
@unpublished{lejay-02-2,
AUTHOR = {Lejay, Antoine},
TITLE = {An introduction to rough paths},
NOTE = {preprint,
\url{http://www.iecn.u-nancy.fr/~lejay/rough.html}},
YEAR = {2002}
}
@inproceedings {levy-51,
AUTHOR = {L{\'e}vy, Paul},
TITLE = {Wiener's random function, and other {L}aplacian random
functions},
BOOKTITLE = {Proceedings of the Second Berkeley Symposium on Mathematical
Statistics and Probability, 1950},
PAGES = {171--187},
PUBLISHER = {University of California Press},
ADDRESS = {Berkeley and Los Angeles},
YEAR = {1951},
MRCLASS = {60.0X},
MRNUMBER = {13,476b}
}
@book {levy-65,
AUTHOR = {L{\'e}vy, Paul},
TITLE = {Processus stochastiques et mouvement brownien},
PUBLISHER = {Gauthier-Villars \& Cie, Paris},
YEAR = {1965},
PAGES = {vi+438},
MRCLASS = {60.00 (60.40)},
MRNUMBER = {32 \#8363}
}
@book {levy-92,
AUTHOR = {L{\'e}vy, Paul},
TITLE = {Processus stochastiques et mouvement brownien},
NOTE = {Followed by a note by M. Lo\`eve, Reprint of the second
(1965) edition},
PUBLISHER = {\'Editions Jacques Gabay},
ADDRESS = {Sceaux},
YEAR = {1992},
PAGES = {iv+437},
ISBN = {2-87647-091-8},
MRCLASS = {60-02 (60G05 60G12 60J65)},
MRNUMBER = {93i:60003},
}
@unpublished{li-lyons-02,
author = {Li, Xiang Dong and Lyons, Terry},
title = {Smoothness of the {I}t\^o map on $p$-rough path spaces
({I}): $1