Normalized stochastic integrals in topological vector spaces
Mikulevicius, Remigijus ; Rozovskii, Boris L.
Séminaire de probabilités de Strasbourg, Tome 32 (1998), p. 137-165 / Harvested from Numdam
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Publié le : 1998-01-01
@article{SPS_1998__32__137_0,
     author = {Mikulevicius, Remigijus and Rozovskii, Boris L.},
     title = {Normalized stochastic integrals in topological vector spaces},
     journal = {S\'eminaire de probabilit\'es de Strasbourg},
     volume = {32},
     year = {1998},
     pages = {137-165},
     mrnumber = {1655149},
     zbl = {0910.60041},
     language = {en},
     url = {http://dml.mathdoc.fr/item/SPS_1998__32__137_0}
}

Mikulevicius, Remigijus; Rozovskii, Boris L. Normalized stochastic integrals in topological vector spaces. Séminaire de probabilités de Strasbourg, Tome 32 (1998) pp. 137-165. http://gdmltest.u-ga.fr/item/SPS_1998__32__137_0/

1. Daletskii, Yu.L., "Infinite dimensional elliptic operators and parabolic equations connected with them," Uspekhi Mat. Nauk, Translations, Russ. Math. Surveys, 22, 1967, pp. 1-53. | MR 223773 | Zbl 0164.41304

2. Detweiler, E., "Banach space valued processes with independent increments and stochastic integration," In: Probability in Banach Spaces IV, Proceedings, Oberwolfach 1982, Lecture Notes in Math. 990, Berlin-Heidelberg-New York, Springer, pp. 54-83. | MR 707509 | Zbl 0514.60010

3. Dunford, N. and Schwartz, J.T., Linear Operators, 1, Interscience Publishers, New York, 1958. | MR 117523 | Zbl 0084.10402

4. Gihman, I.I. and Skorohod, A.V., Stochastic Differential Equations, Springer Verlag, 1972. | MR 346904 | Zbl 0242.60003

5. Grigelionis, B. and Mikulevicius, R., "Stochastic evolution equations and derivatives of the conditional distributions," Lecture Notes in Control and Inf. Sci., 49, 1983, pp. 43-86. | MR 799933 | Zbl 0513.60058

6. Gyöngi, I. and Krylov, N.V. "On stochastic equations with respect to semimartingales I," Stochastics, 4(1), 1980, pp. 1-21. | MR 587426 | Zbl 0439.60061

7. Gyöngi, I. and Krylov, N.V., "On stochastic equations with respect to semimartingles II., "Stochastics, 6(3-4), 1982, pp. 153-173. | MR 665398 | Zbl 0481.60060

8. Jacod, J., "Calcul Stochastique et Problèmes de Martingales," Lecture Notes in Math., 714, Springer-Verlag, Berlin, 1979. | MR 542115 | Zbl 0414.60053

9. Korezlioglu, H., "Stochastic integration for operator valued processes on Hilbert spaces and on nuclear spaces," Stochastics, 24, 1988, pp. 171-213. | MR 972474 | Zbl 0649.60065

10. Krylov, N.V. and Rozovskii, B.L., "Stochastic evolution systems," J. Soviet Math., 16, 1981, pp. 1233-1276. | Zbl 0462.60060

11. Kunita, H., 'Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge, 1990. | MR 1070361 | Zbl 0743.60052

12. Kunita, H., "Stochastic integrals based on martingales taking values in Hilbert space," Nagoya Math. J., 38, 1970, pp. 41-52. | MR 264754 | Zbl 0234.60071

13. Liptser, R.S. and Shiryaev, A.N., Statistics of Random Processes I, Springer-Verlag, Berlin, 1977. | Zbl 0364.60004

14. Meyer, P.A., "Notes sur les intégrales stochastiques I. Intégrales hilbertiennes," Séminaire de Proba XI, Lecture Notes in Math, 581, 1977, pp. 446-463. | Numdam | MR 501333 | Zbl 0374.60071

15. Métivier, M. and Pistone, G. "Une formule d'isométrie pour l'intégrale stochastique hilbertienne et équations d'évolution linéaires stochastiques," Zeitschrift Wahrscheinlichkeitstheorie, 33, 1975, pp. 1-18. | MR 383527 | Zbl 0325.60054

16. Métivier, M. and Pellaumail, J., Stochastic Integration, Academic Press, 1980. | MR 578177 | Zbl 0463.60004

17. Métivier, M., Stochastic Partial Differential Equations in Infinite Dimensional Spaces, Scuola Normale Superiore, Pisa, 1988. | MR 982268 | Zbl 0664.60062

18. Mikulevicius, R. and Rozovskii, B.L., "Uniqueness and absolute continuity of weak solutions for parabolic SPDE's, "Acta Appl. Math., 35, 1994, pp. 179-192. | MR 1286505 | Zbl 0810.60054

19. Mikulevicius, R. and Rozovskii, B.L., "Martingale Problems for Stochastic PDE's", In: "Stochastic Partial Differential Equations. Six Perspectives " R. Carmona and B.L. Rozovskii Ed., AMS, Mathematical Surveys and Monographs series, 1998 (to appear). | MR 1661767 | Zbl 0938.60047

20. Rozovskii, B., Stochastic Evolution Systems, Kluwer Academic Publishers, Dordrecht, 1990. | MR 1135324 | Zbl 0724.60070

21. Schwartz, L., "Sous-espaces hilbertiens d'espaces vectoriels topologiques et noyaux associés (noyaux reproduisants)," Journal d'Analyse Math., 13, 1964, pp. 115-256. | MR 179587 | Zbl 0124.06504

22. Walsh, J.B., "An introduction to partial differential equations," Ecole d'Eté de Probabilités de Saint-Flour XIV, 1984, Lecture Notes in Math., 1180, 1986, pp. 265-439. | MR 876085 | Zbl 0608.60060