Non-Markovian fully coupled forward–backward stochastic systems and classical solutions of path-dependent PDES
نویسندگان
چکیده
منابع مشابه
Comparison of Viscosity Solutions of Fully Nonlinear Degenerate Parabolic Path-Dependent PDEs
We prove a comparison result for viscosity solutions of (possibly degenerate) parabolic fully nonlinear path-dependent PDEs. In contrast with the previous result in Ekren, Touzi & Zhang [10], our conditions are easier to check and allow for the degenerate case, thus including first order path-dependent PDEs. Our argument follows the regularization method as introduced by Jensen, Lions & Sougani...
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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, well-posedness result under an additional...
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The main objective of this paper and the accompanying one [Viscosity solutions of fully nonlinear parabolic path dependent PDEs: Part II (2012) Preprint] is to provide a notion of viscosity solutions for fully nonlinear parabolic path-dependent PDEs. Our definition extends our previous work [Ann. Probab. (2014) 42 204–236], focused on the semilinear case, and is crucially based on the nonlinear...
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This paper provides an overview of the recently developed notion of viscosity solutions of path-dependent partial differential equations. We start by a quick review of the CrandallIshii notion of viscosity solutions, so as to motivate the relevance of our definition in the path-dependent case. We focus on the wellposedness theory of such equations. In particular, we provide a simple presentatio...
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A fully classical limit of the recently published quantum-classical approximation [A. A. Neufeld, J. Chem. Phys. 119, 2488 (2003)] is obtained and analyzed. The resulting kinetic equations are capable of describing the evolution of an open system on the entire time axis, including the short-time non-Markovian stage, and are valid beyond linear response regime. We have shown, that proceeding to ...
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ژورنال
عنوان ژورنال: Stochastic Analysis and Applications
سال: 2020
ISSN: 0736-2994,1532-9356
DOI: 10.1080/07362994.2020.1780135