Approximations of the brownian rough path with applications to stochastic analysis
Annales de l'I.H.P. Probabilités et statistiques (2005)
- Volume: 41, Issue: 4, page 703-724
- ISSN: 0246-0203
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topFriz, Peter, and Victoir, Nicolas. "Approximations of the brownian rough path with applications to stochastic analysis." Annales de l'I.H.P. Probabilités et statistiques 41.4 (2005): 703-724. <http://eudml.org/doc/77863>.
@article{Friz2005,
author = {Friz, Peter, Victoir, Nicolas},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {support theorem; large deviations; modulus of continuity of diffusions},
language = {eng},
number = {4},
pages = {703-724},
publisher = {Elsevier},
title = {Approximations of the brownian rough path with applications to stochastic analysis},
url = {http://eudml.org/doc/77863},
volume = {41},
year = {2005},
}
TY - JOUR
AU - Friz, Peter
AU - Victoir, Nicolas
TI - Approximations of the brownian rough path with applications to stochastic analysis
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2005
PB - Elsevier
VL - 41
IS - 4
SP - 703
EP - 724
LA - eng
KW - support theorem; large deviations; modulus of continuity of diffusions
UR - http://eudml.org/doc/77863
ER -
References
top- [1] S. Aida, S. Kusuoka, D. Stroock, On the support of Wiener functionals, in: Asymptotic Problems in Probability Theory: Wiener Functionals and Asymptotics (Sanda/Kyoto, 1990), Pitman Res. Notes Math. Ser., vol. 284, Longman Sci. Tech., Harlow, 1993, pp. 3-34. Zbl0790.60047MR1354161
- [2] P. Baldi, M. Chaleyat-Maurel, Sur l'équivalent du module de continuité des processus de diffusion, in: Séminaire de Probabilités, XXI, Lecture Notes in Math., vol. 1247, Springer, Berlin, 1987, pp. 404-427. Zbl0617.60034MR941996
- [3] P. Baldi, M. Sanz-Solé, Modulus of continuity for stochastic flows, in: Barcelona Seminar on Stochastic Analysis (St. Feliu de Guíxols, 1991), Progr. Probab., vol. 32, Birkhäuser, Basel, 1993, pp. 1-20. Zbl0798.60041MR1265040
- [4] P. Baldi, G. Ben Arous, G. Kerkyacharian, Large deviations and the Strassen theorem in Hölder norm, Stochastic Process. Appl.42 (1) (1992) 171-180. Zbl0757.60014MR1172514
- [5] G. Ben Arous, M. Ledoux, Grandes déviations de Freidlin–Wentzell en norme hölderienne, in: Séminaire de Probabilités, XXVIII, Lecture Notes in Math., vol. 1583, Springer, Berlin, 1994, pp. 293-299. Zbl0811.60019MR1329119
- [6] G. Ben Arous, M. Gruadinaru, Normes hölderiennes et support des diffusions, C. R. Acad. Sci. Paris Sér. I Math.316 (3) (1993) 283-286. Zbl0768.60067MR1205200
- [7] G. Ben Arous, M. Gruadinaru, M. Ledoux, Hölder norms and the support theorem for diffusions, Ann. Inst. H. Poincaré Probab. Statist.30 (3) (1994) 415-436. Zbl0814.60075MR1288358
- [8] J.-D. Deuschel, D. Stroock, Large Deviations, Academic Press, New York, 1989. Zbl0705.60029MR997938
- [9] A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Jones and Bartlett, Boston, MA, 1993. Zbl0793.60030MR1202429
- [10] M. Eddahbi, M. N'zi, Y. Ouknine, Grandes déviations des diffusions sur les espaces de Besov–Orlicz et application, Stochastics Stochastics Rep.65 (3–4) (1999) 299-315. Zbl0926.60029MR1687624
- [11] G.B. Folland, E.M. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, 1982. Zbl0508.42025MR657581
- [12] P.K. Friz, Continuity of the Itô-map for Hölder rough path with applications to the Support Theorem in Hölder norm, preprint, 2003. MR2202036
- [13] P.K. Friz, N. Victoir, A note on the notion of geometric rough paths, preprint, 2004. Zbl1108.34052
- [14] B. Gaveau, Principe de moindre action, propagation de la chaleur et estimées sous-elliptiques sur certains groupes nilpotents, Acta Math.139 (1–2) (1977) 95-153. Zbl0366.22010MR461589
- [15] M. Gromov, Carnot–Carathéodory spaces seen from within, in: Sub-Riemannian Geometry, Progr. Math., vol. 144, Birkhäuser, Basel, 1996, pp. 79-323. Zbl0864.53025MR1421823
- [16] I. Gyöngy, D. Nualart, M. Sanz-Solé, Approximation and support theorems in modulus spaces, Probab. Theory Related Fields101 (4) (1995) 495-509. Zbl0820.60038MR1327223
- [17] B.M. Hambly, T.J. Lyons, Stochastic area for Brownian motion on the Sierpinski gasket, Ann. Probab.26 (1) (1998) 132-148. Zbl0936.60073MR1617044
- [18] W. Hebisch, A. Sikora, A smooth subadditive homogeneous norm on a homogeneous group, Studia Math.96 (1990) 231-236. Zbl0723.22007MR1067309
- [19] I. Karatzas, E. Shreve, Brownian Motion and Stochastic Calculus, 1991. Zbl0638.60065
- [20] T. Lyons, Differential equations driven by rough signals, Math. Res. Lett.1 (1994) 451-464. Zbl0835.34004MR1302388
- [21] A. Lejay, Introduction to Rough Paths, Séminaire de probabilités, Lecture Notes in Math., vol. XXXVII, Springer-Verlag, 2003. Zbl1041.60051MR2053040
- [22] P. Levy, Processus Stochastiques et Mouvement Brownien, Gauthier-Villars, 1948. Zbl0034.22603MR190953
- [23] T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana14 (2) (1998) 215-310. Zbl0923.34056MR1654527
- [24] T. Lyons, Z. Qian, System Control and Rough Paths, Oxford University Press, 2002. Zbl1029.93001MR2036784
- [25] M. Ledoux, Z. Qian, T. Zhang, Large deviations and support theorem for diffusion processes via rough paths, Stochastic Process. Appl.102 (2) (2002) 265-283. Zbl1075.60510MR1935127
- [26] P. Malliavin, Stochastic Analysis, Grundlehren der Mathematischen Wissenschaften, vol. 313, Springer-Verlag, Berlin, 1997. Zbl0878.60001MR1450093
- [27] M. Mellouk, Support des diffusions dans les espaces de Besov–Orlicz, C. R. Acad. Sci. Paris Sér. I Math.319 (3) (1994) 261-266. Zbl0805.60074MR1288415
- [28] A. Millet, M. Sanz-Solé, A simple proof of the support theorem for diffusion processes, in: Séminaire de Probabilités, XXVIII, Lecture Notes in Math., vol. 1583, Springer, Berlin, 1994, pp. 36-48. Zbl0807.60073MR1329099
- [29] R. Montgomery, A Tour of Subriemannian Geometries, their Geodesics and Applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. Zbl1044.53022MR1867362
- [30] D. Neuenschwander, Probability on the Heisenberg Group, Lecture Notes in Math., Springer, 1996. Zbl0870.60007
- [31] C. Reutenauer, Free Lie Algebras, London Mathematical Society Monographs. New Series, vol. 7, Oxford Science Publications, 1993. Zbl0798.17001MR1231799
- [32] D. Revuz, N. Yor, Continuous Martingales and Brownian Motion, Springer, 2001. Zbl0731.60002
- [33] E.M. Sipilainen, A pathwise view of solutions of stochastic differential equations, PhD Thesis, University of Edinburgh, 1993.
- [34] E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, 1970. Zbl0207.13501MR290095
- [35] D. Stroock, S. Taniguchi, Diffusions as integral curves, or Stratonovich without Itô, in: The Dynkin Festschrift, Progr. Probab., vol. 34, 1994, pp. 333-369. Zbl0814.60074MR1311729
- [36] D. Stroock, S.R. Varadhan, Multidimensional Diffusion Processes, Springer, 1979. Zbl0426.60069MR532498
- [37] D. Stroock, S.R. Varadhan, On the support of diffusion processes with applications to the strong maximum principle, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. III: Probability Theory, 1972, pp. 333-359. Zbl0255.60056MR400425
- [38] S.R.S. Varadhan, Brownian Motion. Lecture notes.
- [39] V.S. Varadarajan, Lie Groups, Lie Algebras and their Presentations, Springer, 1984. Zbl0955.22500MR746308
- [40] N. Victoir, An extension theorem to rough path, preprint, 2003.
- [41] F. Warner, Foundations of Differentiable Manifolds and Lie Groups, Springer, 1983. Zbl0516.58001MR722297
- [42] L.C. Young, An inequality of Hölder type, connected with Stieltjes integration, Acta Math.67 (1936) 251-282. Zbl0016.10404MR1555421
Citations in EuDML Documents
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- P. Friz, T. Lyons, D. Stroock, Lévy's area under conditioning
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- Laure Coutin, Nicolas Victoir, Enhanced Gaussian processes and applications
- Peter Friz, Nicolas Victoir, Differential equations driven by gaussian signals
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