Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data
- INSA de Rennes, IRMAR (France)
Unbounded stochastic control problems may lead to Hamilton-Jacobi-Bellman equations whose Hamiltonians are not always defined, especially when the diffusion term is unbounded with respect to the control. We obtain existence and uniqueness of viscosity solutions growing at most like o(1+ vertical bar x vertical bar {sup p}) at infinity for such HJB equations and more generally for degenerate parabolic equations with a superlinear convex gradient nonlinearity. If the corresponding control problem has a bounded diffusion with respect to the control, then our results apply to a larger class of solutions, namely those growing like O(1+ vertical bar x vertical bar {sup p}) at infinity. This latter case encompasses some equations related to backward stochastic differential equations.
- OSTI ID:
- 22043927
- Journal Information:
- Applied Mathematics and Optimization, Vol. 63, Issue 3; Other Information: Copyright (c) 2011 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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