Abstract
AbstractWe establish a convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs. Our proof is based on a novel convergence theorem for dynamic sublinear expectations and the stochastic representation of viscosity solutions as value functions.
Funder
Albert-Ludwigs-Universität Freiburg im Breisgau
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Aliprantis, C.D., Border, K.B.: Infinite Dimensional Analysis: A Hitchhiker’s Guide, 3rd edn. Springer, Berlin Heidelberg (2006)
2. Backhoff-Veraguas, J., Lacker, D., Tangpi, L.: Nonexponential Sanov and Schilder theorems on Wiener space: BSDEs, Schrödinger Problems and control. Ann. Appl. Probab. 30(3), 1321–1367 (2020)
3. Numerical Analysis and Applications;G Barles,2013
4. Bayraktar, E., Keller, C.: Path-dependent Hamilton–Jacobu equations with super-quadratic growth in the gradient and the vanishing viscosity method. SIAM J. Control. Optim. 60(3), 1690–1711 (2022)
5. Bogachev, V.I.: Measure Theory. Springer, Berlin Heidelberg (2007)