Anticipating integrals for a class of martingales

Bernoulli

Volumn 4, Issue 1, 1998, Pages 81-114

  Ma, Jin ^a   Protter, Philip ^a   Martin, Jaime San ^b  

^a PURDUE UNIVERSITY   (United States)

^b UNIVERSITY OF CHILE   (Chile)

Author keywords

anticipating stochastic differential equation; anticipating stochastic integral; Aze ma's martingale; homogeneous chaos; multiple stochastic integral; normal martingales; stochastic integration by parts; structure equation; variational derivative

Indexed keywords

EID: 0009960281     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.2307/3318533     Document Type: Article

References (16)

1. Barlow, M. (1981) Construction of a martingale with given absolute value. Ann. Probab., 9, 314±320.
2. Buckdahn, R. (1994) Anticipative Girsanov Transformations and Skorohod Stochastic Differential equations, Mem. Amer. Math. Soc., 111 (533).
3. Dellacherie, C. (1972) CapaciteÂs et Processus Stochastiques. Berlin: Springer-Verlag.
4. Dellacherie, C., Maisonneuve, B. and Meyer, P.A. (1992) ProbabiliteÂs et Potentiel: Chapitres XVII aÁ XXIV. Paris: Hermann.
5. Emery, M. (1989) On the AzeÂma martingales. In J. AzeÂma, P.A. Meyer and M. Yor (eds), SeÂm. de Probab. XXIII, Lecture Notes in Math. 1372, pp. 66±87. New York: Springer-Verlag.
6. Kurtz, T.G. and Protter, P. (1991) Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab., 19, 1035±1070.
7. Meyer, P.A. (1976) Un cours sur les inteÂgrales stochastiques. In P.A. Meyer (ed.), SeÂm. de Probab. X, Lecture Notes in Math. 511, pp. 245±400. New York: Springer-Verlag.
8. Meyer, P.A. (1989) Construction de solutions d'equations de structure. In J. AzeÂma, P.A. Meyer and M. Yor (eds), SeÂm. de Probab. XXIII, Lecture Notes in Math. 1372, pp. 142±145. New York: Springer-Verlag.
9. Meyer, P.A. (1993) Quantum Probability for Probabilistics, Lecture Notes in Math. 1538. New York: Springer-Verlag.
10. Nualart, D. and Pardoux, E. (1988) Stochastic calculus with anticipating integrands. Probab. Theory Related Fields, 78, 535±582.
11. Nualart, D. (1995) Malliavin Calculus and Related Topics. New York: Springer-Verlag.
12. Ocone, D. (1984) Malliavin calculus and stochastic integral representation of diffusion processes, Stochastics, 12, 161±185.
13. Protter, P. and Sharpe, M. (1979) Martingales with given absolute value. Ann. Probab., 7, 1056±1058.
14. Protter, P. (1990) Stochastic Integration and Differential Equations. Heidelberg: Springer-Verlag.
15. Russo, F. and Vallois, P. (1994) Product of two multiple stochastic integrals. Preprint.
16. Vallois, P. (1995) Decomposing the Brownian path via the range process. Stochastic Process. Appl., 55, 211±226.