Results 1 to 10 of about 86,831,735 (183)
Continuous dependence estimates for viscosity solutions of integro-PDEs [PDF]
Journal of Differential Equations, 2005 The authors consider the following general nonlinear degenerate parabolic integro-partial differential equation (PDE): \[ \begin{matrix} u_t (t,x)+ F\left( t,x,u(t,x),Du(t,x),D^2 u(t,x), u(t,.)\right)=0,\quad\text{ in } Q_T, \\ u(0,x) = u_0 (x), \quad \text{ in }\mathbb{R}^N,\end{matrix}\tag{1} \] where \( Q_T:= (0,T)\times\mathbb{R}^N, F \;:\overline {
Kenneth H Karlsen +1 more
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Comparison of Viscosity Solutions of Semilinear Path-Dependent PDEs [PDF]
SIAM Journal on Control and Optimization, 2020 This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduced in \cite{EKTZ} which considers as test functions all those smooth processes which are tangent in mean.
Jianfeng Zhang, Zhenjie Ren
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An Overview of Viscosity Solutions of Path-Dependent PDEs [PDF]
Springer Proceedings in Mathematics and Statistics, 2014 This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial di erential equations. We start by a quick review of the Crandall- Ishii notion of viscosity solutions, so as to motivate the relevance of our de nition in the path-dependent case. We focus on the wellposedness theory of such equations.
Nizar Touzi +2 more
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On viscosity solutions of path dependent PDEs
Annals of Probability, 2014 In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac formula to non-Markovian case.
Christian Keller +2 more
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Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part I [PDF]
Annals of Probability, 2016 In our previous paper [Ekren, Touzi and Zhang (2015)], we introduced a notion of viscosity solutions for fully nonlinear path-dependent PDEs, extending the semilinear case of Ekren et al. [Ann. Probab. 42 (2014) 204-236], which satisfies a partial comparison result under standard Lipshitz-type assumptions. The main result of this paper provides a full,
Ibrahim Ekren, Jianfeng Zhang
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Crandall–Lions viscosity solutions for path-dependent PDEs: The case of heat equation [PDF]
Bernoulli, 2022 We address our interest to the development of a theory of viscosity solutions {à} la Crandall-Lions for path-dependent partial differential equations (PDEs), namely PDEs in the space of continuous paths C([0, T ]; R^d). Path-dependent PDEs can play a central role in the study of certain classes of optimal control problems, as for instance optimal ...
Andrea Cosso, Francesco Russo
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Viscosity Solutions of Systems of PDEs with Interconnected Obstacles and Switching Problem [PDF]
Applied Mathematics and Optimization, 2012 This paper deals with existence and uniqueness, in viscosity sense, of a solution for a system of m variational partial differential inequalities with inter-connected obstacles. A particular case of this system is the deterministic version of the Verification Theorem of the Markovian optimal m-states switching problem.
S Hamadène
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Approximate viscosity solutions of path-dependent PDEs and Dupire’s vertical differentiability
Annals of Applied Probability, 2023 We introduce a notion of approximate viscosity solution for a class of nonlinear path-dependent PDEs (PPDEs), including the Hamilton-Jacobi-Bellman type equations. Existence, comparaison and stability results are established under fairly general conditions.
Bouchard Bruno +1 more
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Viscosity Solutions to Second Order Parabolic PDEs on Riemannian Manifolds [PDF]
Acta Applicandae Mathematicae, 2011 In this work we consider viscosity solutions to second order parabolic PDEs $u_{t}+F(t,x,u,du,d^{2}u)=0$ defined on compact Riemannian manifolds with boundary conditions. We prove comparison, uniqueness and existence results for the solutions. Under the assumption that the manifold $M$ has nonnegative sectional curvature, we get the finest results.
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Boundary regularity for viscosity solutions to degenerate elliptic PDEs
Journal of Mathematical Analysis and Applications, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
G Gripenberg
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