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Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data

Journal Article · · Applied Mathematics and Optimization
 [1]
  1. 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, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 63; ISSN 0095-4616
Country of Publication:
United States
Language:
English

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