Rough evolution equations

Annals of Probability

Volumn 38, Issue 1, 2010, Pages 1-75

  Gubinelli, Massimiliano ^a   Tindel, Samy ^b  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b UNIVERSITÉ DE LORRAINE   (France)

Author keywords

Fractional Brownian motion; Rough paths theory; Stochastic PDEs

Indexed keywords

EID: 77953669175     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/08-AOP437     Document Type: Article

References (25)

1. Adams, R. A. (1975). Sobolev Spaces. Pure and Applied Mathematics 65. Academic Press, New York. MR0450957
2. Coutin,L. and QIAN, Z. (2002). Stochastic analysis, rough path analysis and fractional Brownian motions. Probab. Theory Related Fields 122 108-140. MR1883719
3. DALANG, R. C. (1999). Extending the martingale measure stochastic integral with applications to spatially homogeneous s.p.d.e.'s. Electron. J. Probab. 4 no. 6, 29 pp. (electronic). MR1684157
4. FEYEL,D. and DE LA PRADELLE, A. (2006). Curvilinear integrals along enriched paths. Electron. J. Probab. 11 no. 34, 860-892 (electronic). MR2261056
5. FRIZ,P. and VICTOIR, N. Multidimensional dimensional processes seen as rough paths. Cambridge Univ. Press. To appear.
6. GUBINELLI, M. (2004). Controlling rough paths. J. Funct. Anal. 216 86-140. MR2091358
7. GUBINELLI, M. (2006). Rough solutions of the periodic Korteweg-de Vries equation. Preprint.
8. GUBINELLI, M. (2006). Rooted trees for 3D Navier-Stokes equation. Dyn. Partial Differ. Equ. 3 161-172. MR2227041
9. GUBINELLI, M. (2008). Abstract integration, combinatorics of trees and differential equations. Preprint.
10. GUBINELLI, M. (2009). Ramification of rough paths. J. Differential Equations. To appear.
11. GUBINELLI, M. (2009). Rough integrals in higher dimensions. Unpublished manuscript.
12. GUBINELLI,M.,LEJAY,A. and TINDEL, S. (2006). Young integrals and SPDEs. Potential Anal. 25 307-326. MR2255351
13. LEJAY, A. (2003). An introduction to rough paths. In Séminaire de Probabilités XXXVII. Lecture Notes in Math. 1832 1-59. Springer, Berlin. MR2053040
14. LEÓN,J.A. and SAN MARTÍN, J. (2007). Linear stochastic differential equations driven by a fractional Brownian motion with Hurst parameter less than 1/2. Stoch. Anal. Appl. 25 105-126. MR2284483
15. LOTOTSKY,S.V. and ROZOVSKII, B. L. (2006). Wiener chaos solutions of linear stochastic evolution equations. Ann. Probab. 34 638-662. MR2223954
16. LYONS,T. and QIAN, Z. (2002). System Control and Rough Paths. Oxford Univ. Press, Oxford. MR2036784
17. LYONS, T. J. (1998). Differential equations driven by rough signals. Rev. Mat. Iberoamericana 14 215-310. MR1654527
18. MASLOWSKI,B. and NUALART, D. (2003). Evolution equations driven by a fractional Brownian motion. J. Funct. Anal. 202 277-305. MR1994773
19. NUALART, D. (1995). The Malliavin Calculus and Related Topics. Springer, New York. MR1344217
20. PAZY, A. (1983). Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences 44. Springer, New York. MR710486
21. PÉREZ-ABREU,V. and TUDOR, C. (2002). Multiple stochastic fractional integrals: A transfer principle for multiple stochastic fractional integrals. Bol. Soc. Mat. Mexicana (3) 8 187-203. MR1952159
22. QUER-SARDANYONS,L. and TINDEL, S. (2007). The 1-d stochastic wave equation driven by a fractional Brownian sheet. Stochastic Process. Appl. 117 1448-1472. MR2353035
23. TINDEL, S. (1997). Stochastic parabolic equations with anticipative initial condition. Stochastics Stochastics Rep. 62 1-20. MR1489179
24. TINDEL,S.,TUDOR,C.A. and VIENS, F. (2003). Stochastic evolution equations with fractional Brownian motion. Probab. Theory Related Fields 127 186-204. MR2013981
25. WALSH, J. B. (1986). An introduction to stochastic partial differential equations. In École D'été de Probabilités de Saint-Flour, XIV-1984. Lecture Notes in Math. 1180 265-439. Springer, Berlin. MR876085