| [Aze82] |
Robert Azencott.
Formule de Taylor stochastique et développement asymptotique
d'intégrales de Feynman.
In Seminar on Probability, XVI, Supplement, pages 237-285.
Springer, Berlin, 1982. [ bib | MathSciNet ] |
| [BA89] |
Gérard Ben Arous.
Flots et séries de Taylor stochastiques.
Probab. Theory Related Fields, 81(1):29-77, 1989. [ bib | MathSciNet ] |
| [BB00] |
K. Burrage and P. M. Burrage.
Order conditions of stochastic Runge-Kutta methods by
B-series.
SIAM J. Numer. Anal., 38(5):1626-1646 (electronic), 2000. [ bib | MathSciNet ] |
| [BHL01] |
R. F. Bass, Ben Hambly, and Terry Lyons.
Extending the Wong-Zakai theorem to reversible Markov
processes.
preprint, to appear in J. Eur. Math. Soc., 2001. [ bib ] |
| [BL94] |
Nicolas Bouleau and Dominique Lépingle.
Numerical methods for stochastic processes.
John Wiley & Sons Inc., New York, 1994.
A Wiley-Interscience Publication. [ bib | MathSciNet ] |
| [Bou72] |
N. Bourbaki.
Éléments de mathématique. Fasc. XXXVII.
Groupes et algèbres de Lie. Chapitre II: Algèbres de Lie
libres. Chapitre III: Groupes de Lie.
Hermann, Paris, 1972.
Actualités Scientifiques et Industrielles, No. 1349. [ bib | MathSciNet ] |
| [Cas93] |
Fabienne Castell.
Asymptotic expansion of stochastic flows.
Probab. Theory Related Fields, 96(2):225-239, 1993. [ bib | MathSciNet ] |
| [CDM01] |
Mireille Capitaine and Catherine Donati-Martin.
The Lévy area process for the free Brownian motion.
J. Funct. Anal., 179(1):153-169, 2001. [ bib | MathSciNet ] |
| [CG95] |
Fabienne Castell and Jessica Gaines.
An efficient approximation method for stochastic differential
equations by means of the exponential Lie series.
Math. Comput. Simulation, 38(1-3):13-19, 1995.
Probabilités numériques (Paris, 1992). [ bib | MathSciNet ] |
| [CG96] |
Fabienne Castell and Jessica Gaines.
The ordinary differential equation approach to asymptotically
efficient schemes for solution of stochastic differential equations.
Ann. Inst. H. Poincaré Probab. Statist., 32(2):231-250,
1996. [ bib | MathSciNet ] |
| [CG98] |
V. V. Chistyakov and O. E. Galkin.
On maps of bounded p-variation with p>1.
Positivity, 2(1):19-45, 1998. [ bib | MathSciNet ] |
| [Che57] |
Kuo-Tsai Chen.
Integration of paths, geometric invariants and a generalized
Baker-Hausdorff formula.
Ann. of Math. (2), 65:163-178, 1957. [ bib | MathSciNet ] |
| [Che58] |
Kuo-Tsai Chen.
Integration of paths-a faithful representation of paths by
non-commutative formal power series.
Trans. Amer. Math. Soc., 89:395-407, 1958. [ bib | MathSciNet ] |
| [CQ00] |
Laure Coutin and Zhongmin Qian.
Stochastic differential equations for fractional Brownian motions.
C. R. Acad. Sci. Paris Sér. I Math., 331(1):75-80, 2000. [ bib | MathSciNet ] |
| [CQ02] |
Laure Coutin and Zhongmin Qian.
Stochastic analysis, rough path analysis and fractional Brownian
motions.
Probab. Theory Related Fields, 122(1):108-140, 2002. [ bib | MathSciNet ] |
| [DN98] |
R.M. Dudley and R. Norvaisa.
An introduction to p-variation and Young integrals - with
emphasis on sample functions of stochastic processes.
Lecture given at the Centre for Mathematical Physics and
Stochastics, Department of Mathematical Sciences, University of
Aarhus, 1998. [ bib ] |
| [DN99] |
Richard M. Dudley and Rimas Norvaisa.
Differentiability of six operators on nonsmooth functions and
p-variation, volume 1703 of Lecture Notes in Mathematics.
Springer-Verlag, Berlin, 1999.
With the collaboration of Jinghua Qian. [ bib | MathSciNet ] |
| [Dos76] |
Halim Doss.
Liens entre équations différentielles stochastiques et
ordinaires.
C. R. Acad. Sci. Paris Sér. A-B, 283(13):Ai, A939-A942,
1976. [ bib | MathSciNet ] |
| [Dos77] |
Halim Doss.
Liens entre équations différentielles stochastiques et
ordinaires.
Ann. Inst. H. Poincaré Sect. B (N.S.), 13(2):99-125, 1977. [ bib | MathSciNet ] |
| [Föl81] |
H. Föllmer.
Calcul d'Itô sans probabilités.
In Seminar on Probability, XV (Univ. Strasbourg, Strasbourg,
1979/1980) (French), pages 143-150. Springer, Berlin, 1981. [ bib | MathSciNet ] |
| [GL94] |
J. G. Gaines and Terry Lyons.
Random generation of stochastic area integrals.
SIAM J. Appl. Math., 54(4):1132-1146, 1994. [ bib | MathSciNet ] |
| [GL97] |
J. G. Gaines and Terry Lyons.
Variable step size control in the numerical solution of stochastic
differential equations.
SIAM J. Appl. Math., 57(5):1455-1484, 1997. [ bib | MathSciNet ] |
| [HL98] |
Ben Hambly and Terry Lyons.
Stochastic area for Brownian motion on the Sierpinski gasket.
Ann. Probab., 26(1):132-148, 1998. [ bib | MathSciNet ] |
| [HL02] |
Ben Hambly and Terry Lyons.
Uniqueness for the Signature of a Path of Bounded Variation.
Preprint, 2002. [ bib ] |
| [Hu92] |
Yao Zhong Hu.
Série de Taylor stochastique et formule de
Campbell-Hausdorff, d'après Ben Arous.
In Séminaire de Probabilités, XXVI, volume 1526 of
Lecture Notes in Math., pages 579-586. Springer, Berlin, 1992. [ bib | MathSciNet ] |
| [IW81] |
Nobuyuki Ikeda and Shinzo Watanabe.
Stochastic differential equations and diffusion processes.
North-Holland Publishing Co., Amsterdam, 1981. [ bib | MathSciNet ] |
| [IW89] |
Nobuyuki Ikeda and Shinzo Watanabe.
Stochastic differential equations and diffusion processes.
North-Holland Publishing Co., Amsterdam, second edition, 1989. [ bib | MathSciNet ] |
| [KP92] |
Peter Kloeden and Eckhard Platen.
Numerical solution of stochastic differential equations.
Springer-Verlag, Berlin, 1992. [ bib | MathSciNet ] |
| [KPS94] |
Peter Kloeden, Eckhard Platen, and Henri Schurz.
Numerical solution of SDE through computer experiments.
Springer-Verlag, Berlin, 1994.
With 1 IBM-PC floppy disk (3.5 inch; HD). [ bib | MathSciNet ] |
| [Kun80] |
Hiroshi Kunita.
On the representation of solutions of stochastic differential
equations.
In Seminar on Probability, XIV (Paris, 1978/1979) (French),
pages 282-304. Springer, Berlin, 1980. [ bib | MathSciNet ] |
| [Lej02a] |
Antoine Lejay.
An introduction to rough paths.
preprint, http://www.iecn.u-nancy.fr/~lejay/rough.html, 2002. [ bib ] |
| [Lej02b] |
Antoine Lejay.
Stochastic differential equations driven by a processes generated by
divergence form operators.
preprint, http://www.iecn.u-nancy.fr/~lejay/rough.html, 2002. [ bib ] |
| [Lév51] |
Paul Lévy.
Wiener's random function, and other Laplacian random functions.
In Proceedings of the Second Berkeley Symposium on Mathematical
Statistics and Probability, 1950, pages 171-187, Berkeley and Los Angeles,
1951. University of California Press. [ bib | MathSciNet ] |
| [Lév65] |
Paul Lévy.
Processus stochastiques et mouvement brownien.
Gauthier-Villars & Cie, Paris, 1965. [ bib | MathSciNet ] |
| [Lév92] |
Paul Lévy.
Processus stochastiques et mouvement brownien.
Éditions Jacques Gabay, Sceaux, 1992.
Followed by a note by M. Loève, Reprint of the second (1965)
edition. [ bib | MathSciNet ] |
| [LL02a] |
Xiang Dong Li and Terry Lyons.
Smoothness of the Itô map on p-rough path spaces (I):
1<p<2.
preprint, 2002. [ bib ] |
| [LL02b] |
Terry Lyons and Antoine Lejay.
On the importance of the Lévy area for systems controlled by
converging stochastic processes. application to homogenization.
preprint, http://www.iecn.u-nancy.fr/~lejay/rough.html, 2002. [ bib ] |
| [LLQ02] |
Michel Ledoux, Terry Lyons, and Zhongmin Qian.
Lévy area of Wiener processes in Banach spaces.
Ann. Probab., 30(2):546-578, 2002. [ bib | MathSciNet ] |
| [Lot02] |
Sergey Lototsky.
Small perturbation of stochastic parabolic equations: a power series
analysis.
J. Funct. Anal., 193(1):94-115, 2002. [ bib | MathSciNet ] |
| [LQ96] |
Terry Lyons and Zhongmin Qian.
Calculus for multiplicative functionals, Itô's formula and
differential equations.
In Itô's stochastic calculus and probability theory, pages
233-250. Springer, Tokyo, 1996. [ bib | MathSciNet ] |
| [LQ97a] |
Terry Lyons and Zhongmin Qian.
Calculus of variation for multiplicative functionals.
In New trends in stochastic analysis (Charingworth, 1994),
pages 348-374. World Sci. Publishing, River Edge, NJ, 1997. [ bib | MathSciNet ] |
| [LQ97b] |
Terry Lyons and Zhongmin Qian.
A class of vector fields on path spaces.
J. Funct. Anal., 145(1):205-223, 1997. [ bib | MathSciNet ] |
| [LQ97c] |
Terry Lyons and Zhongmin Qian.
Flow equations on spaces of rough paths.
J. Funct. Anal., 149(1):135-159, 1997. [ bib | MathSciNet ] |
| [LQ97d] |
Terry Lyons and Zhongmin Qian.
Stochastic Jacobi fields and vector fields induced by varying area
on path spaces.
Probab. Theory Related Fields, 109(4):539-570, 1997. [ bib | MathSciNet ] |
| [LQ98] |
Terry Lyons and Zhongmin Qian.
Flow of diffeomorphisms induced by a geometric multiplicative
functional.
Probab. Theory Related Fields, 112(1):91-119, 1998. [ bib | MathSciNet ] |
| [LQ02] |
Terry Lyons and Zhongmin Qian.
System Control and Rough Paths.
Oxford University Press, 2002.
Oxford Mathematical Monographs. [ bib ] |
| [LQZ02] |
Michel Ledoux, Zhongmin Qian, and T. Zhang.
Large deviations and support theorem for diffusion processes via
rough paths.
To appear in Stoch. Proc. Appl., 2002. [ bib ] |
| [LS96] |
Terry Lyons and Lucretiu Stoica.
On the limit of stochastic integrals of differential forms.
In Stochastic processes and related topics (Siegmundsberg,
1994), pages 61-66. Gordon and Breach, Yverdon, 1996. [ bib | MathSciNet ] |
| [LS99] |
Terry Lyons and Lucretiu Stoica.
The limits of stochastic integrals of differential forms.
Ann. Probab., 27(1):1-49, 1999. [ bib | MathSciNet ] |
| [LV02] |
Terry Lyons and Nicolas Victoir.
Cubature on Wiener space.
preprint, 2002. [ bib ] |
| [Lyo94] |
Terry Lyons.
Differential equations driven by rough signals. I. An extension
of an inequality of L. C. Young.
Math. Res. Lett., 1(4):451-464, 1994. [ bib | MathSciNet ] |
| [Lyo95] |
Terry Lyons.
The interpretation and solution of ordinary differential equations
driven by rough signals.
In Stochastic analysis (Ithaca, NY, 1993), pages 115-128.
Amer. Math. Soc., Providence, RI, 1995. [ bib | MathSciNet ] |
| [Lyo98] |
Terry Lyons.
Differential equations driven by rough signals.
Rev. Mat. Iberoamericana, 14(2):215-310, 1998. [ bib | MathSciNet ] |
| [LZ99] |
Terry Lyons and Ofer Zeitouni.
Conditional exponential moments for iterated Wiener integrals.
Ann. Probab., 27(4):1738-1749, 1999. [ bib | MathSciNet ] |
| [Mey91] |
P.-A. Meyer.
Sur deux estimations d'intégrales multiples.
In Séminaire de Probabilités, XXV, volume 1485 of
Lecture Notes in Math., pages 425-426. Springer, Berlin, 1991. [ bib | MathSciNet ] |
| [Pla81] |
Eckhard Platen.
A Taylor formula for semimartingales solving a stochastic equation.
In Stochastic differential systems (Visegrád, 1980), pages
157-164. Springer, Berlin, 1981. [ bib | MathSciNet ] |
| [PW82] |
Eckhard Platen and Wolfgang Wagner.
On a Taylor formula for a class of Itô processes.
Probab. Math. Statist., 3(1):37-51 (1983), 1982. [ bib | MathSciNet ] |
| [Reu93] |
Christophe Reutenauer.
Free Lie algebras.
The Clarendon Press Oxford University Press, New York, 1993.
Oxford Science Publications. [ bib | MathSciNet ] |
| [Sip93] |
E.-M. Sipiläinen.
A pathwise view of solutions of stochastic differential
equations.
PhD thesis, University of Edinburgh, 1993. [ bib ] |
| [Str87] |
Robert S. Strichartz.
The Campbell-Baker-Hausdorff-Dynkin formula and solutions of
differential equations.
J. Funct. Anal., 72(2):320-345, 1987. [ bib | MathSciNet ] |
| [Sus78] |
Héctor J. Sussmann.
On the gap between deterministic and stochastic ordinary differential
equations.
Ann. Probability, 6(1):19-41, 1978. [ bib | MathSciNet ] |
| [Var84] |
V. S. Varadarajan.
Lie groups, Lie algebras, and their representations, volume
102 of Graduate Texts in Mathematics.
Springer-Verlag, New York, 1984.
Reprint of the 1974 edition. [ bib | MathSciNet ] |
| [Wil98] |
David R. E. Williams.
Solutions of differential equations driven by càdlàg paths
of finite p-variation.
PhD thesis, Imperial College, London, 1998. [ bib ] |
| [Wil00] |
David R. E. Williams.
Diffeomorphic flows driven by Lévy processes.
preprint, 2000. [ bib ] |
| [Wil01] |
David R. E. Williams.
Path-wise solutions of stochastic differential equations driven by
Lévy processes.
Rev. Mat. Iberoamericana, 17(2):295-329, 2001. [ bib | MathSciNet ] |
| [Yam79] |
Yuiti Yamato.
Stochastic differential equations and nilpotent Lie algebras.
Z. Wahrsch. Verw. Gebiete, 47(2):213-229, 1979. [ bib | MathSciNet ] |
| [You36] |
L. C. Young.
An inequality of Hölder type connected with Stieltjes
integration.
Acta Math., (67):251-282, 1936. [ bib ] |