4 papers · 1 filter
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…
Nonlinear rough Fokker-Planck equations
Fabio Bugini, Peter K. Friz, Wilhelm Stannat
McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding…
Parameter dependent rough SDEs with applications to rough PDEs
Fabio Bugini, Peter K. Friz, Wilhelm Stannat
Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and Lê in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs under…
Malliavin Calculus for rough stochastic differential equations
Fabio Bugini, Michele Coghi, Torstein Nilssen
In this work we show that rough stochastic differential equations (RSDEs), as introduced by Friz, Hocquet, and Lê (2021), are Malliavin differentiable. We use this to prove existen…