Barles, G.; Rouy, E. A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications. (English) Zbl 0919.35009 Commun. Partial Differ. Equations 23, No. 11-12, 1995-2033 (1998). For the fully nonlinear Hamilton-Jacobi-Bellman equation with Dirichlet boundary conditions arising in stochastic optimal control with exit time is considered. The main result concerns a “Strong Comparison Result” which allows to compare discontinuous viscosity sub- and supersolutions of the mentioned HJB equation. To prove that result some rather complicated conditions for the control problems near the boundary are required. The authors discuss difficulties connected with Dirichlet boundary conditions and show how these conditions can be treated. Some possible extentions of the results of the paper are pointed out. Reviewer: W.Kotarski (Sosnowiec) Cited in 32 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35B45 A priori estimates in context of PDEs 35R60 PDEs with randomness, stochastic partial differential equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:Hamilton-Jacobi-Bellman equation; viscosity solutions; comparison theorem; Dirichlet boundary conditions PDFBibTeX XMLCite \textit{G. Barles} and \textit{E. Rouy}, Commun. Partial Differ. Equations 23, No. 11--12, 1995--2033 (1998; Zbl 0919.35009) Full Text: DOI References: [1] DOI: 10.1215/S0012-7094-87-05521-9 · Zbl 0697.35030 · doi:10.1215/S0012-7094-87-05521-9 [2] Ishii H., Ann. Scuola. Norm. Pisa Sci. 16 (4) pp 105– [3] DOI: 10.1137/S0363012993250268 · Zbl 0847.49025 · doi:10.1137/S0363012993250268 [4] DOI: 10.1512/iumj.1994.43.43020 · Zbl 0819.35057 · doi:10.1512/iumj.1994.43.43020 [5] DOI: 10.1007/978-1-4612-6051-6_2 · doi:10.1007/978-1-4612-6051-6_2 [6] DOI: 10.1080/03605308308820301 · Zbl 0716.49023 · doi:10.1080/03605308308820301 [7] DOI: 10.1080/03605308308820301 · Zbl 0716.49023 · doi:10.1080/03605308308820301 [8] Lions P. L., Sélninaire du Collége de France (1985) [9] DOI: 10.1215/S0012-7094-85-05242-1 · Zbl 0599.35025 · doi:10.1215/S0012-7094-85-05242-1 [10] DOI: 10.1137/0324032 · Zbl 0597.49023 · doi:10.1137/0324032 [11] DOI: 10.1007/978-1-4684-0374-9 · doi:10.1007/978-1-4684-0374-9 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.