The first part of this article presents invarlance criteria Ior a sl;ocnasl;lC （lllier^n~x^l ~qu^luu whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived ...The first part of this article presents invarlance criteria Ior a sl;ocnasl;lC （lllier^n~x^l ~qu^luu whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.展开更多
基金Supported by the Grant PN-II-ID-PCE-2011-3-1038,2011(Grant No.208/05.10.2011)
文摘The first part of this article presents invarlance criteria Ior a sl;ocnasl;lC （lllier^n~x^l ~qu^luu whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.
