55 citations · 684 across the 94 of their papers we have counts for
111 papers
A pathwise approach to semilinear SPDEs with Lévy drivers
Dirk Becherer, Peter Friz, Yuchen Sun
We extend the notion of robust viscosity solutions to semilinear rough partial differential equations (RPDEs) of the form \[ \partial_t u + \mathcal{L}_t u + f(t,x,u,σ^{\top}\nabla…
Rough backward stochastic differential equations
Peter K. Friz, Jian Song, Huilin Zhang +1
We develop an intrinsic well-posedness theory for nonlinear backward stochastic differential equations (BSDEs) driven simultaneously by Brownian motion and a (level-) rough path…
Duality for Stochastic Control with non-Markovian Random Coefficients
Peter Bank, Jannis R. Dause, Filippo de Feo +1
We develop novel duality methods for stochastic optimal control problems under two sources of randomness and non-Markovian random coefficients adapted to just one of them. The Hami…
Controlled fields, rough stochastic calculus, and Itô-Wentzell-Alekseev-Gröbner identities
Jannis R. Dause, Peter K. Friz, Arnulf Jentzen +1
We develop a calculus of space-time controlled fields for rough stochastic systems. This approach provides a unified composition rule for evaluating random fields along rough semim…
Talagrand-type transport inequalities for path spaces over Carnot groups
Peter K. Friz, Helena Kremp, Vaios Laschos +2
We consider Talagrand-type transportation inequalities for the law of Brownian motion on Carnot groups. An important example is the lift of standard Brownian motion to the Brownian…
Mean-field games with rough common noise: the linear-quadratic case
Peter K. Friz, Ioannis Gasteratos, Ulrich Horst +1
Motivated by mean-field games (MFG) with common noise on the one hand and pathwise stochastic control theory on the other, we formulate here a linear-quadratic (LQ) MFG with rough…