Rough Paths Bibliography

Preprints, papers in progress and submitted papers:
(as these papers are not the final versions, please do not circulate them without contacting the authors)

• B.M. Hambly and T.J.Lyons: Uniqueness for the signature of a path of bounded variation and continuous analogues for the free group
• A.Lejay: An Introduction to Rough Paths
• P.Friz, T.Lyons, D.Stroock: Lévy's area under conditioning
• A.Lejay, N.Victoir: On (p,q)-rough paths
• T.Lyons, N.Victoir: An Extension Theorem to Rough Paths
• N.Victoir, P.Friz: Approximations of the Brownian Rough Path with Applications to Stochastic Analysis
• N.Victoir, P.Friz: A note on the Notion of Geometric Rough Paths
• A.Lejay, T.Lyons: On the Importance of the Lévy Area for Systems Controlled by Converging Stochastic Processes. Application to Homogenization.
• L.Coutin, A.Lejay: Semi-martingales and rough paths theory
• A.de La Pradelle, D.Feyel: Curvilinear integrals along rough paths
• M.Gubinelli: Controlling Rough Paths
• P.Friz: Continuity of the Ito-map for Hoelder rough paths with applications to the support theorem in Hoelder norm
• A.Lejay: Stochastic Differential Equations driven by processes generated by divergence form operators
• X.D.Li, T.Lyons: Smoothness of Ito map and simulated annealing on path spaces
• S.Aida: Weak Poincare inequalities on domains defined by Brownian rough paths

Published papers:

• N.Victoir: Lévy area for the free Brownian motion: existence and non-existence, J. Funct. Anal, 208, 107-121, 2004
• R.Marty: Theoreme limite pour une equation differentielle a coefficient aleatoire a memoire longue, C.R.Acad.Sci.Paris, 332, 1-4, 2003
• T.Simon: Small deviations in $p$-variation for multidimensional Lévy processes, J. Math. Kyoto Univ. 43, no. 3, 523-565, 2003
• M.Ledoux, Z.Qian, T. Zhang: Large deviations and support theorem for diffusion processes via rough paths, Stoch. Proc. Appl. 102, no. 2, 265-283, 2002
• R.F.Bass, B.M.Hambly and T.J.Lyons: Extending the Wong-Zakai theorem to reversible Markov processes, J. Euro. Math. Soc. 4, 237-269, 2002
• L.Coutin, Z.Qian: Stochastic Analysis, Rough Path Analysis and Fractional Brownian Motion, Probab. Theory Related Fields, 122(1), 108-140, 2002
• T.Lyons, Z.Qian: System control and rough paths, Oxford Mathematical Monographs, Oxford Science Publications, Oxford University Press, Oxford, 2002
• M.Ledoux, T.Lyons, Z.Qian: Lévy area of Wiener processes in Banach spaces, Ann. Probab. 30, no. 2, 546-578, 2002
• A.Lejay: On the Convergence of Stochastic Integrals Driven by Processes Converging on account of a Homogenization Property, Electr. J. of Prob., Vol. 7, Paper 18, 1-18, 2002
• D.R.E.Williams: Path-wise solutions of stochastic differential equations driven by Lévy processes, Rev. Mat. Iberoamericana 17, no. 2, 295--329, 2001
• M.Capitaine, C.Donati-Martin: The Lévy Area Process for the Free Brownian Motion, J. Funct. Anal., 179(1):153-169, 2001
• T.Simon: Support theorem for jump processes, Stoch. Proc. Appl. 89, no. 1, 1--30, 2000
• T.Lyons, O.Zeitouni: Conditional exponential moments for iterated Wiener integrals, Ann. Probab. 27, no. 4, 1738-1749, 1999
• T.Lyons: Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14, no. 2, 215-310, 1998
• B.M.Hambly, T.J.Lyons: Stochastic area for Brownian motion on the Sierpinski gasket, Ann. Probab. 26, no. 1, 132-148, 1998
• T.Lyons, Z.Qian: Flow of diffeomorphisms induced by a geometric multiplicative functional, Probab. Theory Related Fields 112, no. 1, 91-119, 1998
• T.Lyons, Z.Qian: Stochastic Jacobi fields and vector fields induced by varying area on path spaces, Probab. Theory Related Fields 109, no. 4, 539-570, 1997
• T.Lyons, Z.Qian: Flow equations on spaces of rough paths, J. Funct. Anal. 149, no. 1, 135-159, 1997
• T.Lyons, Z.Qian: A class of vector fields on path spaces, J. Funct. Anal. 145, no. 1, 205-223, 1997
• T.Lyons, Z.Qian: Calculus of variation for multiplicative functionals, New trends in stochastic analysis (Charingworth, 1994), 348-374, World Sci. Publishing, River Edge, NJ, 1997
• T.Lyons, Z.Qian: Calculus for multiplicative functionals, Itô's formula and differential equations, Itô's stochastic calculus and probability theory, 233-250, Springer, Tokyo, 1996
• T.Lyons: The interpretation and solution of ordinary differential equations driven by rough signals, Stochastic analysis (Ithaca, NY, 1993), 115--128, Proc. Sympos. Pure Math., 57, Amer. Math. Soc., Providence, RI, 1995
• T.Lyons: Differential equations driven by rough signals. I. An extension of an inequality of L.C.Young, Math. Res. Lett. 1, no. 4, 451-464, 1994
• J.G.Gaines, T.J.Lyons, Random generation of stochastic area integrals, SIAM J. Appl. Math. 54, no. 4, 1132-1146, 1994
• T.Lyons: On the nonexistence of path integrals, Proc. Roy. Soc. London Ser. A, 432, no. 1885, 281-290, 1991

Useful Background and Historic papers:

• M. Fliess Fonctionnelles causales non linéaires et indéterminées non commutatives Bulletin de la Société Mathématique de France, 109 (1981), p. 3-40
• K.T. Chen: Formal Differential Equations Ann.of Math. (2), 73:110-133, 1961
• K.T. Chen: Integration of Paths, Geometric Invariants and a Generalized Baker- Hausdorff Formula Ann.of Math. (2), 65:163-178, 1957
• L.C.Young: An inequality of Hölder type, connected with Stielties integration, Acta Math. 67, 251-282, 1936