202 citations · 210 across the 5 of their papers we have counts for
4 papers · 1 filter
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 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…
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…
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…