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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.PR2015★ 3 cited
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…
math.PR2014★ 5 cited
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…