Normalized stochastic integrals in topological vector spaces

Remigijus Mikulevicius; Boris L. Rozovskii

Séminaire de probabilités de Strasbourg (1998)

  • Volume: 32, page 137-165

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Mikulevicius, Remigijus, and Rozovskii, Boris L.. "Normalized stochastic integrals in topological vector spaces." Séminaire de probabilités de Strasbourg 32 (1998): 137-165. <http://eudml.org/doc/113980>.

@article{Mikulevicius1998,
author = {Mikulevicius, Remigijus, Rozovskii, Boris L.},
journal = {Séminaire de probabilités de Strasbourg},
keywords = {convex topological vector space; locally square integrable cylindrical martingale; stable space; Hilbert-valued stochastic integrals; stochastic integrals; orthogonal martingale measures; stochastic flows; integration of vector-valued functions},
language = {eng},
pages = {137-165},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Normalized stochastic integrals in topological vector spaces},
url = {http://eudml.org/doc/113980},
volume = {32},
year = {1998},
}

TY - JOUR
AU - Mikulevicius, Remigijus
AU - Rozovskii, Boris L.
TI - Normalized stochastic integrals in topological vector spaces
JO - Séminaire de probabilités de Strasbourg
PY - 1998
PB - Springer - Lecture Notes in Mathematics
VL - 32
SP - 137
EP - 165
LA - eng
KW - convex topological vector space; locally square integrable cylindrical martingale; stable space; Hilbert-valued stochastic integrals; stochastic integrals; orthogonal martingale measures; stochastic flows; integration of vector-valued functions
UR - http://eudml.org/doc/113980
ER -

References

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  1. 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. Zbl0164.41304MR223773
  2. 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. Zbl0514.60010MR707509
  3. 3. Dunford, N. and Schwartz, J.T., Linear Operators, 1, Interscience Publishers, New York, 1958. Zbl0084.10402MR117523
  4. 4. Gihman, I.I.and Skorohod, A.V., Stochastic Differential Equations, Springer Verlag, 1972. Zbl0242.60003MR346904
  5. 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. Zbl0513.60058MR799933
  6. 6. Gyöngi, I. and Krylov, N.V. "On stochastic equations with respect to semimartingales I," Stochastics, 4(1), 1980, pp. 1-21. Zbl0439.60061MR587426
  7. 7. Gyöngi, I. and Krylov, N.V., "On stochastic equations with respect to semimartingles II., "Stochastics, 6(3-4), 1982, pp. 153-173. Zbl0481.60060MR665398
  8. 8. Jacod, J., "Calcul Stochastique et Problèmes de Martingales," Lecture Notes in Math., 714, Springer-Verlag, Berlin, 1979. Zbl0414.60053MR542115
  9. 9. Korezlioglu, H., "Stochastic integration for operator valued processes on Hilbert spaces and on nuclear spaces," Stochastics, 24, 1988, pp. 171-213. Zbl0649.60065MR972474
  10. 10. Krylov, N.V. and Rozovskii, B.L., "Stochastic evolution systems," J. Soviet Math., 16, 1981, pp. 1233-1276. Zbl0462.60060
  11. 11. Kunita, H., 'Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge, 1990. Zbl0743.60052MR1070361
  12. 12. Kunita, H., "Stochastic integrals based on martingales taking values in Hilbert space," Nagoya Math. J., 38, 1970, pp. 41-52. Zbl0234.60071MR264754
  13. 13. Liptser, R.S.and Shiryaev, A.N., Statistics of Random Processes I, Springer-Verlag, Berlin, 1977. Zbl0364.60004
  14. 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. Zbl0374.60071MR501333
  15. 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. Zbl0325.60054MR383527
  16. 16. Métivier, M. and Pellaumail, J., Stochastic Integration, Academic Press, 1980. Zbl0463.60004MR578177
  17. 17. Métivier, M., Stochastic Partial Differential Equations in Infinite Dimensional Spaces, Scuola Normale Superiore, Pisa, 1988. Zbl0664.60062MR982268
  18. 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. Zbl0810.60054MR1286505
  19. 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). Zbl0938.60047MR1661767
  20. 20. Rozovskii, B., Stochastic Evolution Systems, Kluwer Academic Publishers, Dordrecht, 1990. Zbl0724.60070MR1135324
  21. 21. Schwartz, L., "Sous-espaces hilbertiens d'espaces vectoriels topologiques et noyaux associés (noyaux reproduisants)," Journal d'Analyse Math., 13, 1964, pp. 115-256. Zbl0124.06504MR179587
  22. 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. Zbl0608.60060MR876085

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