@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= {Springer}, ADDRESS = {Berlin}, YEAR = {1982}, MRCLASS = {60H10 (58C20 58G32 60J60 81C35)}, MRNUMBER = {84a:60065} } @UNPUBLISHED{bass-hambly-lyons-01, AUTHOR = {Bass, R. F. and Hambly, Ben and Lyons, Terry}, TITLE = {Extending the {W}ong-{Z}akai theorem to reversible {M}arkov processes},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@ARTICLE{lototsky-02, AUTHOR = {Lototsky, Sergey}, TITLE = {Small perturbation of stochastic parabolic equations: a power series analysis}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {193}, YEAR = {2002}, NUMBER = {1}, PAGES = {94--115}, ISSN = {0022-1236}, CODEN = {JFUAAW}, MRCLASS = {60H15 (35B20 35R60 60J60)}, MRNUMBER = {1 923 630} } @ARTICLE{lyons-94, AUTHOR = {Lyons, Terry}, TITLE = {Differential equations driven by rough signals. {I}. {A}n extension of an inequality of {L}. {C}. {Y}oung}, JOURNAL = {Math. Res. Lett.}, FJOURNAL = {Mathematical Research Letters}, VOLUME = {1}, YEAR = {1994}, NUMBER = {4}, PAGES = {451--464}, ISSN = {1073-2780}, MRCLASS = {60H10}, MRNUMBER = {96b:60150} } @INCOLLECTION{lyons-95, AUTHOR = {Lyons, Terry}, TITLE = {The interpretation and solution of ordinary differential equations driven by rough signals}, BOOKTITLE = {Stochastic analysis (Ithaca, NY, 1993)}, PAGES = {115--128}, PUBLISHER = {Amer. Math. Soc.}, ADDRESS = {Providence, RI}, YEAR = {1995}, MRCLASS = {34F05 (60H05 60H10)}, MRNUMBER = {96d:34076} } @ARTICLE{lyons-98, AUTHOR = {Lyons, Terry}, TITLE = {Differential equations driven by rough signals}, JOURNAL = {Rev. Mat. Iberoamericana}, FJOURNAL = {Revista Matem\'atica Iberoamericana}, VOLUME = 14, YEAR = 1998, NUMBER = 2, PAGES = {215--310}, ISSN = {0213-2230}, MRCLASS = {60H10 (34A99 34F05 37H99)}, MRNUMBER = {2000c:60089} } @UNPUBLISHED{lyons-lejay-02, AUTHOR = {Lyons, Terry and Lejay, Antoine}, TITLE = {On the importance of the {L}\'evy area for systems controlled by converging stochastic processes. Application to homogenization}, NOTE = {preprint, \url{http://www.iecn.u-nancy.fr/~lejay/rough.html}}, YEAR = {2002} } @BOOK{lyons-qian-02, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {System {C}ontrol and {R}ough {P}aths}, NOTE = {Oxford Mathematical Monographs}, PUBLISHER = {Oxford University Press}, YEAR = {2002}, PAGES = {250}, ISBN = {0-19-850648-1} } @INCOLLECTION{lyons-qian-96, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {Calculus for multiplicative functionals, {I}t\^o's formula and differential equations}, BOOKTITLE = {It\^o's stochastic calculus and probability theory}, PAGES = {233--250}, PUBLISHER = {Springer}, ADDRESS = {Tokyo}, YEAR = {1996}, MRCLASS = {60H99}, MRNUMBER = {98k:60111} } @ARTICLE{lyons-qian-97-0, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {A class of vector fields on path spaces}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = 145, YEAR = 1997, NUMBER = 1, PAGES = {205--223}, ISSN = {0022-1236}, CODEN = {JFUAAW}, MRCLASS = {60H07 (31C12 58G32)}, MRNUMBER = {98d:60107} } @ARTICLE{lyons-qian-97-1, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {Stochastic {J}acobi fields and vector fields induced by varying area on path spaces}, JOURNAL = {Probab. Theory Related Fields}, FJOURNAL = {Probability Theory and Related Fields}, VOLUME = {109}, YEAR = {1997}, NUMBER = {4}, PAGES = {539--570}, ISSN = {0178-8051}, CODEN = {PTRFEU}, MRCLASS = {60D05 (28D05 58G32 60H07)}, MRNUMBER = {98m:60016} } @ARTICLE{lyons-qian-97-2, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {Flow equations on spaces of rough paths}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {149}, YEAR = {1997}, NUMBER = {1}, PAGES = {135--159}, ISSN = {0022-1236}, CODEN = {JFUAAW}, MRCLASS = {58G32 (60H05)}, MRNUMBER = {99b:58241} } @INCOLLECTION{lyons-qian-97-3, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {Calculus of variation for multiplicative functionals}, BOOKTITLE = {New trends in stochastic analysis (Charingworth, 1994)}, PAGES = {348--374}, PUBLISHER = {World Sci. Publishing}, ADDRESS = {River Edge, NJ}, YEAR = {1997}, MRCLASS = {60H07 (60J57)}, MRNUMBER = {2000k:60112} } @ARTICLE{lyons-qian-98, AUTHOR = {Lyons, Terry and Qian, Zhongmin}, TITLE = {Flow of diffeomorphisms induced by a geometric multiplicative functional}, JOURNAL = {Probab. Theory Related Fields}, FJOURNAL = {Probability Theory and Related Fields}, VOLUME = {112}, YEAR = {1998}, NUMBER = {1}, PAGES = {91--119}, ISSN = {0178-8051}, CODEN = {PTRFEU}, MRCLASS = {60H10 (58G32)}, MRNUMBER = {99k:60153} } @INCOLLECTION{lyons-stoica-96, AUTHOR = {Lyons, Terry and Stoica, Lucre{\c{t}}iu}, TITLE = {On the limit of stochastic integrals of differential forms}, BOOKTITLE = {Stochastic processes and related topics (Siegmundsberg, 1994)}, PAGES = {61--66}, PUBLISHER = {Gordon and Breach}, ADDRESS = {Yverdon}, YEAR = {1996}, MRCLASS = {60H05 (31C25 47N30 58G32)}, MRNUMBER = {97e:60088} } @ARTICLE{lyons-stoica-99, AUTHOR = {Lyons, Terry and Stoica, Lucre{\c{t}}iu}, TITLE = {The limits of stochastic integrals of differential forms}, JOURNAL = {Ann. Probab.}, FJOURNAL = {The Annals of Probability}, VOLUME = {27}, YEAR = {1999}, NUMBER = {1}, PAGES = {1--49}, ISSN = {0091-1798}, CODEN = {APBYAE}, MRCLASS = {58J65 (60H05)}, MRNUMBER = {2000e:58054} } @UNPUBLISHED{lyons-victoir-02, AUTHOR = {Lyons, Terry and Victoir, Nicolas}, TITLE = {Cubature on {W}iener space}, NOTE = {preprint}, YEAR = {2002} } @ARTICLE{lyons-zeitouni-99, AUTHOR = {Lyons, Terry and Zeitouni, Ofer}, TITLE = {Conditional exponential moments for iterated {W}iener integrals}, JOURNAL = {Ann. Probab.}, FJOURNAL = {The Annals of Probability}, VOLUME = {27}, YEAR = {1999}, NUMBER = {4}, PAGES = {1738--1749}, ISSN = {0091-1798}, CODEN = {APBYAE}, MRCLASS = {60J65 (60E15 60H05 60J60)}, MRNUMBER = {2001g:60198} } @INCOLLECTION{meyer-91, AUTHOR = {Meyer, P.-A.}, TITLE = {Sur deux estimations d'int\'egrales multiples}, BOOKTITLE = {S\'eminaire de Probabilit\'es, XXV}, SERIES = {Lecture Notes in Math.}, VOLUME = {1485}, PAGES = {425--426}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1991}, MRCLASS = {60H05}, MRNUMBER = {93m:60107} } @INCOLLECTION{platen-81, AUTHOR = {Platen, Eckhard}, TITLE = {A {T}aylor formula for semimartingales solving a stochastic equation}, BOOKTITLE = {Stochastic differential systems (Visegr\'ad, 1980)}, PAGES = {157--164}, PUBLISHER = {Springer}, ADDRESS = {Berlin}, YEAR = {1981}, MRCLASS = {60H10 (60G44)}, MRNUMBER = {83g:60071} } @ARTICLE{platen-wagner-82, AUTHOR = {Platen, Eckhard and Wagner, Wolfgang}, TITLE = {On a {T}aylor formula for a class of {I}t\^o processes}, JOURNAL = {Probab. Math. Statist.}, FJOURNAL = {Probability and Mathematical Statistics}, VOLUME = {3}, YEAR = {1982}, NUMBER = {1}, PAGES = {37--51 (1983)}, ISSN = {0208-4147}, MRCLASS = {60H10}, MRNUMBER = {85m:60107} } @BOOK{reutenauer-93, AUTHOR = {Reutenauer, Christophe}, TITLE = {Free {L}ie algebras}, NOTE = {Oxford Science Publications}, PUBLISHER = {The Clarendon Press Oxford University Press}, ADDRESS = {New York}, YEAR = {1993}, PAGES = {xviii+269}, ISBN = {0-19-853679-8}, MRCLASS = {17-02 (05-02 17B05)}, MRNUMBER = {94j:17002} } @PHDTHESIS{sipilainen-93, AUTHOR = {Sipil\"ainen, E.-M.}, TITLE = {A pathwise view of solutions of stochastic differential equations}, SCHOOL = {University of Edinburgh}, YEAR = {1993} } @ARTICLE{strichartz-87, AUTHOR = {Strichartz, Robert S.}, TITLE = {The {C}ampbell-{B}aker-{H}ausdorff-{D}ynkin formula and solutions of differential equations}, JOURNAL = {J. Funct. Anal.}, FJOURNAL = {Journal of Functional Analysis}, VOLUME = {72}, YEAR = {1987}, NUMBER = {2}, PAGES = {320--345}, ISSN = {0022-1236}, CODEN = {JFUAAW}, MRCLASS = {22E15 (34A25 34A45 34C40 53C20 58F99)}, MRNUMBER = {89b:22011}, MRREVIEWER = {Hans Plesner Jakobsen} } @ARTICLE{sussmann-78, AUTHOR = {Sussmann, H{\'e}ctor J.}, TITLE = {On the gap between deterministic and stochastic ordinary differential equations}, JOURNAL = {Ann. Probability}, VOLUME = {6}, YEAR = {1978}, NUMBER = {1}, PAGES = {19--41}, MRCLASS = {60H10 (34F05)}, MRNUMBER = {57 \#1649} } @BOOK{varadarajan-84, AUTHOR = {Varadarajan, V. S.}, TITLE = {Lie groups, {L}ie algebras, and their representations}, SERIES = {Graduate Texts in Mathematics}, VOLUME = {102}, NOTE = {Reprint of the 1974 edition}, PUBLISHER = {Springer-Verlag}, ADDRESS = {New York}, YEAR = {1984}, PAGES = {xiii+430}, ISBN = {0-387-90969-9}, MRCLASS = {22-01 (17-01)}, MRNUMBER = {85e:22001} } @UNPUBLISHED{williams-00, AUTHOR = {Williams, David R. E.}, TITLE = {Diffeomorphic flows driven by {L}\'evy processes}, NOTE = {preprint}, YEAR = {2000} } @ARTICLE{williams-01, AUTHOR = {Williams, David R. E.}, TITLE = {Path-wise solutions of stochastic differential equations driven by {L}\'evy processes}, JOURNAL = {Rev. Mat. Iberoamericana}, FJOURNAL = {Revista Matem\'atica Iberoamericana}, VOLUME = {17}, YEAR = {2001}, NUMBER = {2}, PAGES = {295--329}, ISSN = {0213-2230}, MRCLASS = {60H20 (60G51)}, MRNUMBER = {1 891 200} } @PHDTHESIS{williams-98, AUTHOR = {Williams, David R. E.}, TITLE = {Solutions of differential equations driven by c\`adl\`ag paths of finite $p$-variation}, SCHOOL = {Imperial College, London}, YEAR = {1998} } @ARTICLE{yamato-79, AUTHOR = {Yamato, Yuiti}, TITLE = {Stochastic differential equations and nilpotent {L}ie algebras}, JOURNAL = {Z. Wahrsch. Verw. Gebiete}, FJOURNAL = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie und Verwandte Gebiete}, VOLUME = {47}, YEAR = {1979}, NUMBER = {2}, PAGES = {213--229}, ISSN = {0044-3719}, MRCLASS = {60H10 (58G32 60J60)}, MRNUMBER = {82f:60143} } @ARTICLE{young-36, AUTHOR = {Young, L. C.}, TITLE = {An inequality of {H}\"older type connected with {S}tieltjes integration}, JOURNAL = {Acta Math.}, NUMBER = {67}, YEAR = {1936}, PAGES = {251--282} }