Change of variable formulas for non-anticipative functionals on path space

Journal of Functional Analysis

Volumn 259, Issue 4, 2010, Pages 1043-1072

  Cont, Rama ^a,b   Fournié, David Antoine ^c  

^a SORBONNE UNIVERSITÉ   (France)

^b Department of Earth and Environmental Sciences   (United States)

^c NONE   (United States)

Author keywords

Cadlag functions; Dirichlet process; Functional calculus; Functional derivative; It formula; Malliavin calculus; Quadratic variation; Semimartingale; Stochastic integral

Indexed keywords

EID: 77952953212     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2010.04.017     Document Type: Article

References (17)

1. Billingsey P. Convergence of Probability Measures 1999, Wiley, Princeton, NJ.
2. Cont R., Fournié D.-A. A functional extension of the Itô formula. C. R. Math. Acad. Sci. Paris Ser. I 2010, 348:57-61.
3. Cont R., Fournié D.-A. Functional Itô calculus and stochastic integral representation of martingales working paper. arxiv:/1002.2446.
4. Coquet F., Mémin J., Słomiński L. On non-continuous Dirichlet processes. J. Theoret. Probab. 2003, 16:197-216.
5. Dellacherie C., Meyer P.-A. Probabilities and Potential. North-Holland Math. Stud. 1978, vol. 29. North-Holland Publishing Co., Amsterdam.
6. B. Dupire, Functional Itô calculus, Portfolio Research Paper 2009-04, Bloomberg, 2009.
7. Föllmer H. Calcul d'Itô sans probabilités. Lecture Notes in Math. 1981, vol. 850:143-150. Springer, Berlin.
8. Föllmer H. Dirichlet processes. Lecture Notes in Math. 1981, vol. 851:476-478. Springer, Berlin.
9. Itô K. On a stochastic integral equation. Proc. Imp. Acad. Tokyo 1944, 20:519-524.
10. Jacod J., Shiryaev A.N. Limit Theorems for Stochastic Processes 2003, Springer-Verlag, Berlin. second ed.
11. Lyons T.J., Zhang T.S. Decomposition of Dirichlet processes and its application. Ann. Probab. 1994, 22:494-524.
12. Malliavin P. Stochastic Analysis 1997, Springer.
13. Meyer P. Un cours sur les integrales stochastiques. Lecture Notes in Math. 1976, vol. 511:245-400. Springer, Berlin.
14. Protter P.E. Stochastic Integration and Differential Equations 2005, Springer-Verlag, Berlin. second ed.
15. Russo F., Vallois P. Elements of stochastic calculus via regularization. Lecture Notes in Math. 2007, vol. 1899:147-185. Springer, Berlin.
16. Stricker C. Variation conditionnelle des processus stochastiques. Ann. Inst. H. Poincaré Probab. Statist. 1988, 24:295-305.
17. Stroock D.W. The Malliavin calculus, a functional analytic approach. J. Funct. Anal. 1981, 44:212-257.