Uniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data

Abstract : 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 $o(1+|x|^p)$ 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 $O(1+|x|^p)$ at infinity. This latter case encompasses some equations related to backward stochastic differential equations.
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https://hal.archives-ouvertes.fr/hal-00327496
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Soumis le : mercredi 8 octobre 2008 - 15:34:04
Dernière modification le : mercredi 12 juillet 2017 - 01:15:04
Document(s) archivé(s) le : jeudi 3 juin 2010 - 21:17:01

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  • HAL Id : hal-00327496, version 1
  • ARXIV : 0810.1435

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Francesca Da Lio, Olivier Ley. Uniqueness results for convex Hamilton-Jacobi equations under $p>1$ growth conditions on data. 2008. <hal-00327496>

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