Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on Data |
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Authors: | Francesca Da Lio Olivier Ley |
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Institution: | 1.Dipartimento di Matematica Pura e Applicata,Padova,Italy;2.IRMAR,INSA de Rennes,Rennes,France |
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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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Keywords: | |
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