Lévy's area under conditioning

P. Friz; T. Lyons; D. Stroock

Annales de l'I.H.P. Probabilités et statistiques (2006)

  • Volume: 42, Issue: 1, page 89-101
  • ISSN: 0246-0203

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Friz, P., Lyons, T., and Stroock, D.. "Lévy's area under conditioning." Annales de l'I.H.P. Probabilités et statistiques 42.1 (2006): 89-101. <http://eudml.org/doc/77889>.

@article{Friz2006,
author = {Friz, P., Lyons, T., Stroock, D.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Hölder topology; support theorem; rough path; Brownian motion},
language = {eng},
number = {1},
pages = {89-101},
publisher = {Elsevier},
title = {Lévy's area under conditioning},
url = {http://eudml.org/doc/77889},
volume = {42},
year = {2006},
}

TY - JOUR
AU - Friz, P.
AU - Lyons, T.
AU - Stroock, D.
TI - Lévy's area under conditioning
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2006
PB - Elsevier
VL - 42
IS - 1
SP - 89
EP - 101
LA - eng
KW - Hölder topology; support theorem; rough path; Brownian motion
UR - http://eudml.org/doc/77889
ER -

References

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  1. [1] G. Ben Arous, M. Gradinaru, Normes hölderiennes et support des diffusions, C. R. Acad. Sci. Paris Sér. I Math.16 (3) (1993) 283-286. Zbl0768.60067MR1205200
  2. [2] G. Ben Arous, M. Gradinaru, M. Ledoux, Hölder norms and the support theorem for diffusions, Ann. Inst. H. Poincaré Probab. Statist.30 (3) (1994) 415-436. Zbl0814.60075MR1288358
  3. [3] P. Friz, Continuity of the Itô-map for Hölder rough path with applications to the support theorem in Hölder norm, Preprint, 2003, in press. MR2202036
  4. [4] P. Friz, N. Victoir, Approximations of the Brownian rough path with applications to stochastic analysis, Preprint, 2003, in press. Zbl1080.60021
  5. [5] 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
  6. [6] A. Lejay, Introduction to rough paths, in: Séminaire de probabilités, vol. XXXVII, Lecture Notes in Math., vol. 1583, 2003, pp. 36-48. Zbl1041.60051MR2053040
  7. [7] A. Lejay, N. Victoir, On ( p , q ) -rough paths, Preprint, 2004. Zbl1097.60048MR2228694
  8. [8] T. Lyons, Differential equations driven by rough signals, Math. Res. Lett.1 (1994) 451-464. Zbl0835.34004MR1302388
  9. [9] T. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana14 (2) (1998) 215-310. Zbl0923.34056MR1654527
  10. [10] T. Lyons, Z. Qian, System Control and Rough Paths, Oxford University Press, 2002. Zbl1029.93001MR2036784
  11. [11] A. Millet, M. Sanz-Sole, A simple proof of the support theorem for diffusion processes, in: Séminaire de probabilités, vol. XXVIII, Lecture Notes in Math., vol. 1583, Springer, Berlin, 1994, pp. 36-48. Zbl0807.60073MR1329099
  12. [12] E. Sipilainen, A pathwise view of solutions of stochastic differential equations, Ph.D. Thesis, University of Edinburgh, 1993. 
  13. [13] D. Stroock, Markov Processes from K. Itô's Perspective, Princeton University Press, 2003. Zbl1070.60003MR1980149
  14. [14] 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
  15. [15] D. Stroock, S. 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, 1970, pp. 333-359. Zbl0255.60056MR400425
  16. [16] D. Stroock, S. Varadhan, On degenerate elliptic-parabolic operators of second order and their associated diffusions, Comm. Pure Appl. Math.XXII (1972) 651-714. Zbl0344.35041MR387812

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