ﻻ يوجد ملخص باللغة العربية
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. It is also consistent with smooth solutions when the dimension is less or equal to two, or the non-linearity is concave in the second order space derivative. We finally investigate the regularity (in the sense of Dupire) of the solution to the PPDE.
This paper introduces a convenient solution space for the uniformly elliptic fully nonlinear path dependent PDEs. It provides a wellposedness result under standard Lipschitz-type assumptions on the nonlinearity and an additional assumption formulated
We address our interest to the development of a theory of viscosity solutions {`a} 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
In this article, we adapt the definition of viscosity solutions to the obstacle problem for fully nonlinear path-dependent PDEs with data uniformly continuous in $(t,omega)$, and generator Lipschitz continuous in $(y,z,gamma)$. We prove that our defi
We consider a large family of integro-differential equations and establish a non-local counterpart of Hopfs lemma, directly expressed in terms of the symbol of the operator. As closely related problems, we also obtain a variety of maximum principles
We propose a definition of viscosity solutions to fully nonlinear PDEs driven by a rough path via appropriate notions of test functions and rough jets. These objects will be defined as controlled processes with respect to the driving rough path. We s