3 papers
math.AP2022
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…
math.PR2021
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…
math.AP2017
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…