Strong and weak solutions to stochastic inclusions

Kisielewicz, Michał

Banach Center Publications, Tome 31 (1995), p. 277-286 / Harvested from The Polish Digital Mathematics Library

Résumé

Existence of strong and weak solutions to stochastic inclusions $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{ℝ^{n}} H_{τ, z} (x_{τ}) q (d τ, d z)$ and $x_{t} - x_{s} \in \int_{s}^{t} F_{τ} (x_{τ}) d τ + \int_{s}^{t} G_{τ} (x_{τ}) d w_{τ} + \int_{s}^{t} \int_{| z | \leq 1} H_{τ, z} (x_{τ}) q (d τ, d z) + \int_{s}^{t} \int_{| z | > 1} H_{τ, z} (x_{τ}) p (d τ, d z)$ , where p and q are certain random measures, is considered.

Publié le : 1995-01-01

Zbl 0837.93068

EUDML-ID : urn:eudml:doc:262679

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     author = {Kisielewicz, Micha\l },
     title = {Strong and weak solutions to stochastic inclusions},
     journal = {Banach Center Publications},
     volume = {31},
     year = {1995},
     pages = {277-286},
     zbl = {0837.93068},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p277bwm}
}

Kisielewicz, Michał. Strong and weak solutions to stochastic inclusions. Banach Center Publications, Tome 31 (1995) pp. 277-286. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv32z1p277bwm/

Bibliographie

[000] [1] A. V. Skorohod, Studies in the Theory of Random Processes, Dover, New York, 1982.

[001] [2] M. Kisielewicz, Differential Inclusions and Optimal Control, Kluwer Acad. Publ. and Polish Sci. Publ., Warszawa-Dordrecht, 1991. | Zbl 0731.49001

[002] [3] M. Kisielewicz, Properties of solution set of stochastic inclusions, J. Appl. Math. Stochastic Anal. 6 (1993), 217-236. | Zbl 0796.93106

[003] [4] M. Kisielewicz, Existence of strong solutions to stochastic inclusions, Discuss. Math. 15 (submitted).

[004] [5] P. Protter, Stochastic Integration and Differential Equations, Springer, Berlin, 1990.