75.

Lyons, T., Systems Controlled by Rough paths, European Congress of Mathematicians 2004, European Mathematical Society, 2005,  269-282

74.

Lejay, A., Lyons, T., On the Importance of the L´evy Area for Studying the Limits of Functions of Converging Stochastic Processes. Application to Homogenization. In "Current Trends in Potential Theory. Conference Proceedings, Bucharest, September 2002 and 2003") To appear, The Theta Foundation, Bucharest 2005, 30pp
http://www.maths.ox.ac.uk/~tlyons/pdf/lejay-lyons.pdf

73.

Li, X.D., Lyons, T.J., Smoothness of Itô maps and diffusion processes on path spaces (I) 32pp
http://www.maths.ox.ac.uk/~tlyons/pdf/lilyonsi-2.pdf

72.

Lyons, T.J.,Victoir, N., An Extension Theorem to Rough Paths,
http://www.maths.ox.ac.uk/~tlyons/pdf/Lyons_Victoir_Extension.pdf

71.

St Flour 2004 “Rough Paths” Preliminary hand, detailed, but handwritten notes are at http://sag.maths.ox.ac.uk/tlyons/st_flour/index.htm  
The final latex versions are currently being prepared with assistance from Michael Caruana and Thierry Levy.

70.

Lyons, T.J. and Hambly, B.M., Uniqueness for the signature of a path of bounded variation and continuous analogues of the free group arXiv:math.CA/0507536 (Currently being extended and rewritten to add extra material)
http://www.maths.ox.ac.uk/~tlyons/pdf/identcor7sw.pdf  

69.

Lyons,  T.J., Sidorova N On the radius of convergence of the log signature, 21pp Submitted to the Doob Memorial Volume of the Illinois Journal of Mathematics
http://www.maths.ox.ac.uk/~tlyons/pdf/lyons_sidorova.pdf

68.

Friz, P., Lyons, T., Stroock, D., Lévy’s area under conditioning, anihpb2142, available online and to appear in the Annals of the Institute Poincare, 13pp
http://www.maths.ox.ac.uk/~tlyons/pdf/Friz_Lyons_stroock.pdf

67.

Lyons, T.J. and Yam, P., On Gauss-Green Theorem and Boundaries of a class of Holder Domains accepted for publication in: Journal de Mathematiques Pures et Appliquees, 20pp.
http://www.maths.ox.ac.uk/~tlyons/pdf/gaussgreen.pdf

66.

Lyons,  T.J.,Sidorova N., Sound compression - a rough path approach, Proceedings of the 4th International Symposium on Information and Communication Technologies, 223-229, Cape Town, January 2005
http://www.maths.ox.ac.uk/~tlyons/pdf/lyons_sidorova_capetown.pdf

65.

Lyons, T.J.,Victoir, N.,Cubature on Wiener space Proc. R. Soc. Lond. A (2004) 460,  169-198.

64.

Bass, R.F., Hambly, B.M., Lyons,T.J., Extending the Wong-Zakai theorem to reversible Markov processes. J.Eur.Math.Soc.(2002), no.4, 237-269.

63.

Crisan, D., Lyons, T.J., Optimal Filtering on Discrete Sets. Numerical Methods.and Stochastics, The Fields Institute for Research in Mathematical Sciences, 34, American Mathematical Society, 21-28, (2002).

62.

Ledoux, M.; Lyons, T.; Qian, Z. Lévy area of Wiener processes in Banach spaces. Ann. Probab., 30 (2002), no. 2, 546-578.

61.

Lyons, T.J., System Control and Rough Paths. Numerical Methods.and Stochastics, The Fields Institute for Research in Mathematical Sciences, 34, American Mathematical Society, 91-100, (2002).

60.

Lyons, T.J., Derivatives as Tradeable Assets. Seminario de Matematica Financiera II, MEFF, 2, 213-232, (1998), (1999).

59.

Lyons, T.J., Smith, A.T., Uncertain Volatility. Risk Magazine, September,(1999), 106-109.

58.

Crisan, D., Lyons, T.J., Minimal entropy approximations and optimal algorithms. Monte Carlo Methods Appl., 8 (2002), no. 4, 343-355.

57.

Crisan, D., Del Moral, P., Lyons, T. J., Interacting particle systems approximations of the Kushner-Stratonovitch equation. Adv. in Appl. Probab., 31 (1999), no. 3, 819-838.

56.

Crisan, D., Del Moral, P., Lyons, T.J., Discrete filtering using branching and interacting particle systems. Markov Process. Related Fields, 5 (1999), no. 3, 293-318.

55.

Crisan, D., Lyons, T.J., A particle approximation of the solution of the Kushner-Stratonovitch equation. Probab. Theory Related Fields 115 (1999), no. 4, 549-578.

54.

Lyons, T.J., Stoica, L., The limits of stochastic integrals of differential forms. Ann. Probab. 27 (1999), no. 1, 1-49.

53.

Lyons, T.J., Zeitouni, O., Conditional exponential moments for iterated Wiener integrals. Ann. Probab. 27 (1999), no. 4, 1738-1749.

52.

Lunt, J., Lyons, T. J., Zhang, T. S., Integrability of functionals of Dirichlet processes, probabilistic representations of semi groups, and estimates of heat kernels. J. Funct. Anal. 153 (1998), no. 2, 320-342.

51.

Crisan, D., Gaines, J., Lyons, T.J., Convergence of a branching particle method to the solution of the Zakai equation. SIAM J. Appl. Math. 58 (1998), no. 5, 1568-1590.

50.

Hambly, B.M., Lyons, T. J., Stochastic area for Brownian motion on the Sierpinski gasket. Ann. Probab. 26 (1998), no. 1, 13-148.

49.

Lyons, T.J., Qian, Z., Flow of diffeomorphisms induced by a geometric multiplicative functional. Probab. Theory Related Fields 112 (1998), no. 1, 91-119.

48.

Lyons, T. J., Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 (1998), no. 2, 215-310.

47.

Lyons, T.J., Qian, Z., Stochastic Jacobi fields and vector fields induced by varying area on path spaces. Probab. Theory Related Fields, 109 (1997), no. 4, 539-570.

46.

Lyons, T.J., Qian, Z., Flow equations on spaces of rough paths. J. Funct. Anal. 149 (1997), no. 1, 135-159.

45.

Lyons, T. J., Qian, Z. M,. A class of vector fields on path spaces. J. Funct. Anal. 145 (1997), no. 1, 205-223.

44.

Crisan, D., Lyons, T.J., Nonlinear filtering and measure-valued processes. Probab. Theory Related Fields. 109 (1997), no. 2, 217-244.

43.

Gaines, J. G., Lyons, T. J., Variable step size control in the numerical solution of stochastic differential equations. SIAM J. Appl. Math. 57 (1997), no. 5, 1455-1484.

42.

Lyons, T. J., Röckner, M., Zhang, T. S., Martingale decomposition of Dirichlet processes on the Banach space $C\sb 0[0,1]$. Stochastic Process. Appl. 64 (1996), no. 1, 31-38.

41.

Lyons, T.J., Qian, Z. M., Calculus for multiplicative functionals, Itô's formula and differential equations. Itô's stochastic calculus and probability theory, (1996). 233-250, Springer, Tokyo.

40.

Lyons, T.J., Zhang, T., Convergence of non-symmetric Dirichlet processes. Stochastics Stochastics Rep. 57 (1996), no. 3-4, 159-167.

39.

Albeverio, S., Lyons, T.J,  Rozanov, Y., Boundary conditions for stochastic evolution equations with an extremely chaotic source. (Russian) Mat. Sb. 186 (1995), no. 12, 3-20; translation in Sb. Math. 186 (1995), no. 12, 1693-1709.

38.

Lyons, T.J., Uncertain volatility and the risk-free sysnthesis of derivatives. Appl.Math.F.(1995),no. 2, 117-133.

37.

Lyons, T. J., Qian, Z. M., Calculus of variation for multiplicative functionals. New trends in stochastic analysis (Charingworth, 1994), 348-374, World Sci. Publishing, River Edge, NJ, (1997).

36.

Lyons, T.J., Stoica, L., On the limit of stochastic integrals of differential forms. Stochastic processes and related topics (Siegmundsberg, 1994), 61-66, Stochastics Monogr., 10, Gordon and Breach, Yverdon, (1996).

35.

Lyons, T. J., 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).

34.

Lyons, T.J., Differential equations driven by rough signals. I. An extension of an inequality of L. C. Young. Math. Res. Lett. 1 (1994), no. 4, 451-464.

33.

Gaines, J. G., Lyons, T. J. Random generation of stochastic area integrals. SIAM J.  Appl. Math. 54 (1994), no. 4, 1132-1146.

32.

Lyons, T. J., Zhang, T. S., Decomposition of Dirichlet processes and its application. Ann. Probab. 22 (1994), no. 1, 494-524.

31.

Lyons, T. J., Zhang, T. S., Note on convergence of Dirichlet processes. Bull. London Math. Soc. 25 (1993), no. 4, 353-356.

30.

Duplantier, B., Lawler, G. F., Le Gall, J.-F., Lyons, T. J., The geometry of the Brownian curve. Bull. Sci. Math. 117 (1993), no. 1, 91-106.

29.

Lyons, T.J., Röckner, M., A note on tightness of capacities associated with Dirichlet forms. Bull. London Math. Soc. 24 (1992), no. 2, 181-184.

28.

Lyons, T.J., Random thoughts on reversible potential theory. Summer School in Potential Theory (Joensuu, 1990), 71-114, Joensuun Yliop. Luonnont. Julk., 26, Univ. Joensuu, Joensuu, (1992).

27.

Erëmenko, A. È., Lyons, T.J., Finely open sets in the limit set of a finitely generated Kleinian group. Approximation by solutions of partial differentialequations (Hanstholm, 1991), 61-67, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 365, Kluwer Acad. Publ., Dordrecht, (1992).

26.

Lyons, T.J., Instability of the conservative property under quasi-isometries. J. Differential Geom. 34 (1991), no. 2, 483-489.

25.

Lyons, T.J.,On the nonexistence of path integrals. Proc. Roy. Soc. London Ser. A 432 (1991), no. 1885, 281-290.

24.

Hayman, W. K., Lyons, T. J., Bases for positive continuous functions. J. London Math. Soc. (2) 42 (1990), no. 2, 292-308.

23.

Lyons, T. J., Zheng, W., A. On conditional diffusion processes. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 3-4, 24-255.

22.

Lyons, T. J., Zheng, W., A. Diffusion processes with nonsmooth diffusion coefficients and their density functions. Proc. Roy. Soc. Edinburgh Sect. A 115 (1990), no. 3-4, 231-242.

21.

Lyons, T.J., A synthetic proof of Makarov's law of the iterated logarithm. Bull. London Math. Soc. 22 (1990), no. 2, 159-162.

20.

Lyons, T.J., Zheng, W., An A crossing estimate for the canonical process on a Dirichlet space and a tightness result. Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987). Astérisque No. 157-158 (1988), 249-271.

19.

Lyons, T. J., What you can do with $n$ observations. Geometrization of statistical theory (Lancaster, 1987), 209-218, ULDM Publ., Lancaster, (1987).

18.

Lyons, T.J., Instability of the Liouville property for quasi-isometric Riemannian manifolds and reversible Markov chains. J. Differential Geom. 26 (1987), no. 1, 33-66.

17.

Lyons, T. J., Reversible diffusion processes on manifolds. Proceedings of the 1st World Congress of the Bernoulli Society, 1 (Tashkent, 1986), 297-305, VNU Sci. Press, Utrecht, (1987).

16.

Lyons, T. J.,The critical dimension at which quasi-every Brownian path is self-avoiding. Adv. in Appl. Probab. (1986), suppl., 87-99.

15.

Barnett, C., Lyons, T.J., Stopping noncommutative processes. Math. Proc. Cambridge Philos. Soc. 99 (1986), no. 1, 151-161.

14.

Lyons, T. J., Reuter, G. E. H., On exponential bounds for solutions of second order differential equations. Bull. London Math. Soc. 17 (1985), no. 2, 139-143.

13.

Lyons, T.J., Sullivan, D., Function theory, random paths and covering spaces. J. Differential Geom. 19 (1984), no. 2, 299-323.

12.

Lyons, T. J., MacGibbon, K. B.,Taylor, J. C., Projection theorems for hitting probabilities and a theorem of Littlewood. J. Funct. Anal. 59 (1984), no.3, 470-489.

11.

Lyons, T.J., Finely harmonic functions need not be quasi-analytic. Bull. London Math. Soc. 16 (1984), no. 4, 413-415.

10.

Lyons, T.J., An application of fine potential theory to prove a Phragmén-Lindelöf theorem. Ann. Inst. Fourier, (Grenoble) 34 (1984), no. 2, 63-66.

9.

Hayman, W.K., Kershaw, D., Lyons, T. J. The best harmonic approximant to a continuous function.  Anniversary volume on approximation theory and functional analysis (Oberwolfach, 1983), 317-327, Internat. Schriftenreihe Numer. Math., 65, Birkhäuser, Basel, 1984.

8.

Lyons, T. J., McKean, H. P., Winding of the plane Brownian motion. Adv. in Math. 51 (1984), no. 3, 21-225.

7.

Lyons, T.J., A simple criterion for transience of a reversible Markov chain. Ann. Probab. 11 (1983), no. 2, 39-402.

6.

Gamelin, T.W., Lyons, T. J., Jensen measures for $R(K)$. J. London Math. Soc. (2) 27 (1983), no. 2, 317-330.

5.

Lyons, T. J., Cones of lower semicontinuous functions and a characterisation of finely hyperharmonic functions. Math. Ann. 261 (1982), no. 3, 293-297.

4.

Lyons, T. J., Finely holomorphic functions. Aspects of contemporary complex analysis (Proc. NATO Adv. Study Inst., Univ. Durham, Durham, 1979), Academic Press, London-New York, (1980), 451-459.

3.

Lyons, T.J., A definition of ${\rm BMO}\sb{p}$ for an abstract harmonic space and a John-Nirenberg theorem. Bull. London Math. Soc. 12 (1980), no. 2, 127-129.

2.

Lyons, T. J., A theorem in fine potential theory and applications to finely holomorphic functions. J. Funct. Anal. 37 (1980), no.1, 19-26.

1.

Lyons, T. J., Finely holomorphic functions. J. Funct. Anal. 37 (1980), no.1, 1-18.