Geodesic
The predictable representation property of compensated-covariation stable families of martingales
Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 1, pp. 99-130 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

@article{TVP_2015_60_1_a4,
     author = {P. Di Tella and H.-J. Engelbert},
     title = {The predictable representation property of compensated-covariation stable families of martingales},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {99--130},
     year = {2015},
     volume = {60},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a4/}
}
TY  - JOUR
AU  - P. Di Tella
AU  - H.-J. Engelbert
TI  - The predictable representation property of compensated-covariation stable families of martingales
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2015
SP  - 99
EP  - 130
VL  - 60
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a4/
LA  - en
ID  - TVP_2015_60_1_a4
ER  - 
%0 Journal Article
%A P. Di Tella
%A H.-J. Engelbert
%T The predictable representation property of compensated-covariation stable families of martingales
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2015
%P 99-130
%V 60
%N 1
%U http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a4/
%G en
%F TVP_2015_60_1_a4
P. Di Tella; H.-J. Engelbert. The predictable representation property of compensated-covariation stable families of martingales. Teoriâ veroâtnostej i ee primeneniâ, Tome 60 (2015) no. 1, pp. 99-130. http://geodesic.mathdoc.fr/item/TVP_2015_60_1_a4/

[1] Boel R., Varaiya P., Wong E., “Martingales on jump processes. I: Representation results”, SIAM J. Control Optim., 13:5 (1975), 999–1021 | MR | Zbl

[2] Clark J. M. C., “The representation of functionals of Brownian motion by stochastic integrals”, Ann. Math. Statist., 41:4 (1970), 1282–1295 | MR | Zbl

[3] Chou C. S., Meyer P.-A., “Sur la répresentation des martingales comme intégrales stochastique dans les processus ponctuels”, Lecture Notes in Math., 465, 1975, 226–236 | MR | Zbl

[4] Davis M. A. H., Varaiya P., “The multiplicity of an increasing family of $\Sigma$-fields”, Ann. Probab., 2:5 (1974), 958–963 | MR | Zbl

[5] Davis M. A. H., “The representation of martingales of jump processes”, SIAM J. Control Optim., 14:4 (1976), 623–638 | DOI | MR | Zbl

[6] Dellacherie C., Meyer P.-A., Probabilities and Potential, North-Holland Math. Stud., 29, North-Holland, Amsterdam–New York, 1978, 189 pp. | MR | Zbl

[7] Elliott R. J., “Stochastic integrals for martingales of a jump process with partially accessible jump times”, Z. Wahrscheinlichkeitstheor. verw. Geb., 36:3 (1976), 213–266 | DOI | MR

[8] Engelbert H. J., Hess J., “Stochastic integrals of continuous local martingales. I; II”, Math. Nachr., 97 (1980), 325–343 ; 100 (1981), 249–269 | MR | Zbl | DOI | MR | Zbl

[9] Galchuk L. I., “Predstavlenie nekotorykh martingalov”, Teoriya veroyatn. i ee primen., 21:3 (1976), 613–620 | MR

[10] Gikhman I. I., Skorokhod A. V., Teoriya sluchainykh protsessov, v. 1, Nauka, M., 1971, 664 pp. | MR

[11] Itô K., “Multiple Wiener integral”, J. Math. Soc. Japan, 3:1 (1951), 157–169 | DOI | MR | Zbl

[12] Itô K., “Spectral type of the shift transformation of differential processes with stationary increments”, Trans. Amer. Math. Soc., 81 (1956), 253–263 | DOI | MR | Zbl

[13] Jacod J., “Calcul stochastique et problèmes de martingales”, Lecture Notes in Math., 714, 1979, 1–539 | MR

[14] Jacod J., Shiryaev A., Limit Theorems for Stochastic Processes, Grundlehren Math. Wiss., 288, Springer-Verlag, Berlin, 2003, 661 pp. | MR | Zbl

[15] Jacod J., Yor M., “Étude des solutions extrémales et représentation intégrale des solutions pour certains problèmes de martingales”, Z. Wahrscheinlichkeitstheor. verw. Geb., 38 (1977), 83–125 | DOI | MR | Zbl

[16] Kabanov Yu. M., “Predstavlenie funktsionalov ot vinerovskogo i puassonovskogo protsessov v vide stokhasticheskikh integralov”, Teoriya veroyatn. i ee primen., 18:2 (1973), 376–380 | MR | Zbl

[17] Kabanov Yu. M., “Integralnye predstavleniya funktsionalov ot protsessov s nezavisimymi prirascheniyami”, Teoriya veroyatn. i ee primen., 19:4 (1974), 889–893 | MR | Zbl

[18] Kallenberg O., Foundations of Modern Probability, Springer-Verlag, New York, 2002, 638 pp. | MR | Zbl

[19] Kunita H., “Representation of martingales with jumps and applications to finance”, Stochastic Analysis and Related Topics, Adv. Stud. Pure Math., 41, Math. Soc. Japan, Tokyo, 2004, 209–232 | MR | Zbl

[20] Kunita H., Watanabe S., “On square integrable martingales”, Nagoya Math. J., 30 (1967), 209–245 | MR | Zbl

[21] Nualart D., Schoutens W., “Chaotic and predictable representations for Lévy processes”, Stochastic Process. Appl., 90:1 (2000), 109–122 | MR | Zbl

[22] Sato K., Lévy Processes and Infinitely Divisible Distributions, Cambridge Stud. Adv. Math., 68, Cambridge Univ. Press, Cambridge, 1999, 521 pp. | MR

[23] Sharpe M., General Theory of Markov Processes, Pure Appl. Math., 133, Academic Press, Boston, 1988, 419 pp. | MR | Zbl

[24] Wang J., “Some remarks on processes with independent increments”, Lecture Notes in Math., 850, 1981, 627–631 | MR | Zbl

[25] Wojtaszczyk P., A Mathematical Introduction to Wavelets, London Math. Soc. Stud. Texts, 37, Cambridge Univ. Press, Cambridge, 1997, 261 pp. | MR | Zbl