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math.PR2025
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…
math.PR2025
Randomisation of rough stochastic differential equations
Peter K. Friz, Khoa Le, Huilin Zhang
Rough stochastic differential equations (RSDEs) are common generalisations of Ito SDEs and Lyons RDEs and have emerged as new tool in several areas of applied probability, includin…
math.PR2024
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…