13 papers · 1 filter
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…
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…
Rough stochastic filtering
Fabio Bugini, Peter K. Friz, Khoa Lê +1
This article is concerned with the well-posedness of the "filtering equations", due to Zakai and Kushner-Stratonovich, arising in nonlinear stochastic filtering. In general situati…
Rough stochastic differential equations
Peter K. Friz, Antoine Hocquet, Khoa Lê
We establish a simultaneous generalization of Itô's theory of stochastic and Lyons' theory of rough differential equations. The interest in such a unification comes from a variety…
Controlled rough SDEs, pathwise stochastic control and dynamic programming principles
Peter K. Friz, Khoa Lê, Huilin Zhang
We study stochastic optimal control of rough stochastic differential equations (RSDEs). This is in the spirit of the pathwise control problem (Lions--Souganidis 1998, Buckdahn--Ma…