202 citations · 210 across the 5 of their papers we have counts for
7 papers
Mean viability theorems and second-order Hamilton-Jacobi equations
Christian Keller
We introduce the notion of mean viability for controlled stochastic differential equations and establish counterparts of Nagumo's classical viability theorems (necessary and suffic…
Path-dependent Hamilton-Jacobi equations with super-quadratic growth in the gradient and the vanishing viscosity method
Erhan Bayraktar, Christian Keller
The non-exponential Schilder-type theorem in Backhoff-Veraguas, Lacker and Tangpi [Ann. Appl. Probab., 30 (2020), pp. 1321-1367] is expressed as a convergence result for path-depen…
Path-dependent Hamilton-Jacobi equations in infinite dimensions
Erhan Bayraktar, Christian Keller
We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main…
Fully nonlinear stochastic and rough PDEs: Classical and viscosity solutions
Rainer Buckdahn, Christian Keller, Jin Ma +1
We study fully nonlinear second-order (forward) stochastic partial differential equations (SPDEs). They can also be viewed as forward path-dependent PDEs (PPDEs) and will be treate…
Viscosity Solutions of Path-dependent Integro-differential Equations
Christian Keller
We extend the notion of viscosity solutions for path-dependent PDEs introduced by Ekren et al. [Ann. Probab. 42 (2014), no. 1, 204-236] to path-dependent integro-differential equat…
Pathwise Itô Calculus for Rough Paths and Rough PDEs with Path Dependent Coefficients
Christian Keller, Jianfeng Zhang
This paper introduces the path derivatives, in the spirit of Dupire's functional Itô calculus, for the controlled paths in the rough path theory with possibly non-geometric rough p…
On viscosity solutions of path dependent PDEs
Ibrahim Ekren, Christian Keller, Nizar Touzi +1
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 SDE…