Explicit form and robustness of martingale representations

Annals of Probability

Volumn 28, Issue 4, 2000, Pages 1747-1780

  Jacod, Jean ^a   Méléard, Sylvie ^b   Protter, Philip ^c  

^a SORBONNE UNIVERSITÉ   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^c Department of Obstetrics Gynecology   (United States)

Author keywords

Clark Haussmann formula; Martingale representation; Stability; Weak convergence

Indexed keywords

EID: 0039771995     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/aop/1019160506     Document Type: Article

References (14)

1. BASS, R., EISENBAUM, N. and SHI, Z. (2000). The most visited sites of symmetric stable processes. Probab. Theory Related Fields 116 391-404.
2. BERTOIN, J. (1996). Lévy Processes. Cambridge Univ. Press.
3. DYNKIN E. B. (1983). Local times and quantum fields. In Seminar on Stochastic Processes 1982 (E. Çinlar, K. L. Chung and R. K. Getoor, eds.) 69-84. Birkhäuser, Boston.
4. EISENBAUM, N. (1994). Dynkin's isomorphism theorem and the Ray-Knight theorems. Probab. Theory Related Fields 99 321-335.
5. EISENBAUM, N. (1997). Théorèmes limites pour les temps locaux d'un processus stable symétrique. Séminaire de Probabilités XXXI. Lecture Notes in Math. 1655 216-224. Springer, Berlin. (Errata: Séminaire de Probabilités XXXIII. Lecture Notes in Math. 1709 417).
6. EISENBAUM, N. and KASPI, H. (1993). A necessary and sufficient condition for the Markov property of the local time process. Ann. Probab. 21 1591-1598.
7. FITZSIMMONS, P. and PITMAN, J. H. (1999). Kac's moment formula and the Feyman-Kac formula for additive functionals of a Markov process. Stochastic Process Appl. 79 117-134.
8. MARCUS, M. B. (2000). The most visited sites of certain Lévy processes. J. Theoret. Probab. To appear.
9. MARCUS, M. B. and ROSEN, J. (1992). Sample path properties of the local times of strongly symmetric Markov processes via Gaussian processes. Ann. Probab. 20 1603-1684.
10. MARCUS, M. B. and ROSEN, J. (1996). Gaussian chaos and sample path properties of additive functionals of symmetric Markov processes Ann. Probab. 24 1130-1177.
11. MARCUS, M. B. and ROSEN J. (2000). Gaussian processes and the local times of symmetric Lévy processes. In Lévy Processes and Their Applications (O. Barnsdorff-Nielsen, T. Mikosch and S. Resnick, eds.) Birkhauser, Boston. To appear.
12. MITRO, J. B. (1979). Dual Markov functionals: applications of a useful auxiliary process. Z. Wahrsch. Verw. Gebiete 48 976-114.
13. REVUZ, D. and YOR, M. (1999). Continuous Martingales and Brownian Motion, 3rd ed. Springer, Berlin.
14. WALSH, J. B. (1972). Markov processes and their functionals in duality. Z. Wahrsch. Verw. Gebiete 24 229-246.