Viscosity Solutions of Stochastic Hamilton--Jacobi--Bellman Equations
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چکیده
منابع مشابه
Stochastic Differential Games and Viscosity Solutions of Hamilton--Jacobi--Bellman--Isaacs Equations
In this paper we study zero-sum two-player stochastic differential games with the help of theory of Backward Stochastic Differential Equations (BSDEs). At the one hand we generalize the results of the pioneer work of Fleming and Souganidis [8] by considering cost functionals defined by controlled BSDEs and by allowing the admissible control processes to depend on events occurring before the beg...
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Problems involving Hamilton-Jacobi equations-which we take to be either of the stationary form H(x, u, Du) = 0 or of the evolution form u, + H(x, t, u, Du) = 0, where Du is the spatial gradient of u-arise in many contexts. Classical analysis of associated problems under boundary and/or initial conditions by the method of characteristics is limited to local considerations owing to the crossing o...
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We consider the Dirichlet problem for Hamilton-Jacobi equations and prove existence, uniqueness and continuous dependence on boundary data of Lipschitz continuous maximal viscosity solutions.
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A theory of viscosity solutions in metric spaces based on local slopes was initiated in [39]. In this manuscript we deepen the study of [39] and present a more complete account of the theory of metric viscosity solutions of Hamilton–Jacobi equations. Several comparison and existence results are proved and the main techniques for such metric viscosity solutions are illustrated.
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2018
ISSN: 0363-0129,1095-7138
DOI: 10.1137/17m1148232