Michta, Mariusz Stochastic inclusions with multivalued integrators. (English) Zbl 1018.60042 Stochastic Anal. Appl. 20, No. 4, 847-862 (2002). Set-valued semimartingales are introduced as an extension of single-valued ones. For such multivalued processes \(X\), a set-valued stochastic integral is defined. Its selection properties are studied. Finally, a stochastic inclusion, with mixed type of integrals \[ z_t-z_s\in\text{cl}_{L^2(\Omega)}\int^t_s G(z)dy + \int^t_s f(z)dX,\quad 0\leq s<t<\infty, \] is considered. Reviewer: Zagorka Lozanov-Crvenković (Novi Sad) Cited in 8 Documents MSC: 60G20 Generalized stochastic processes 60G44 Martingales with continuous parameter 54C60 Set-valued maps in general topology Keywords:stochastic integrals; set-valued stochastic processes; selection; stochastic inclusion; martingales PDFBibTeX XMLCite \textit{M. Michta}, Stochastic Anal. Appl. 20, No. 4, 847--862 (2002; Zbl 1018.60042) Full Text: DOI References: [1] Aubin J.P., Differential Inclusions (1984) · Zbl 0538.34007 · doi:10.1007/978-3-642-69512-4 [2] Bocsan G, On Wiener Stochastic Integral of Multifunction, Seminarul de Teoria Probabilitatilor si Applicatii (1987) [3] DOI: 10.1016/0047-259X(91)90012-Q · Zbl 0746.60051 · doi:10.1016/0047-259X(91)90012-Q [4] Hiai F., Multivalued Stochastic Integrals and Stochastic Differential Inclusions [5] DOI: 10.1016/0047-259X(77)90037-9 · Zbl 0368.60006 · doi:10.1016/0047-259X(77)90037-9 [6] Kisielewicz M., JAMSA 6 pp 217– (1993) [7] DOI: 10.1080/07362999708809507 · Zbl 0891.93070 · doi:10.1080/07362999708809507 [8] Kisielewicz M., Differential Inclusions and Optimal Control (1991) [9] Kisielewicz M., Discuss. Math. Diff. Incl. 15 pp 179– (1995) [10] Michta M., Discuss. Math. Diff. Incl. 16 pp 161– (1996) [11] Michta M., JAMSA 11 pp 73– (1998) [12] DOI: 10.1006/jmaa.1995.1163 · Zbl 0826.60053 · doi:10.1006/jmaa.1995.1163 [13] Motyl J., JAMSA 8 (1995) [14] Murphy J.J., Technical Analysis of the Futures Markets. A Comprehensive Guide to Trading Methods and Applications (1991) [15] Protter Ph., Stochastic Integration and Differential Equations: New Approach (1990) · doi:10.1007/978-3-662-02619-9 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.