caa a22 4500 606193979 CHVBK 20210128100912.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0343-0 doi (NATIONALLICENCE)springer-10.1007/s00030-015-0343-0 Zubov's method for controlled diffusions with state constraints [Elektronische Daten] [Lars Grüne, Athena Picarelli] We consider a controlled stochastic system in presence of state-constraints. Under the assumption of exponential stabilizability of the system near a target set, we aim to characterize the set of points which can be asymptotically driven by an admissible control to the target with positive probability. We show that this set can be characterized as a level set of the optimal value function of a suitable unconstrained optimal control problem which in turn is the unique viscosity solution of a second order PDE which can thus be interpreted as a generalized Zubov equation. Springer Basel, 2015 Controllability for diffusion systems nationallicence Hamilton-Jacobi-Bellman equations nationallicence Viscosity solutions nationallicence Stochastic optimal control nationallicence Grüne Lars Universität Bayreuth, Universitätstrasse 30, 95440, Bayreuth, Germany aut Picarelli Athena Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, OX2 6GG, Oxford, UK aut Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1765-1799 1021-9722 22:6<1765 2015 22 30 https://doi.org/10.1007/s00030-015-0343-0 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0343-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grüne Lars Universität Bayreuth, Universitätstrasse 30, 95440, Bayreuth, Germany aut NATIONALLICENCE 700 1- Picarelli Athena Mathematical Institute, University of Oxford, Andrew Wiles Building, Woodstock Road, OX2 6GG, Oxford, UK aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1765-1799 1021-9722 22:6<1765 2015 22 30