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Stochastic inclusions with multivalued integrators. (English) Zbl 1018.60042

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.

MSC:

60G20 Generalized stochastic processes
60G44 Martingales with continuous parameter
54C60 Set-valued maps in general topology
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