On smooth approximations of rough vector fields and the selection of flows

2019/02/02 by Gennaro Ciampa, Ciampa, Gennaro, Gianluca Crippa +3
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Banach Space Theory #Advanced Numerical Analysis Techniques #Analysis of PDEs (math.AP) #FOS: Mathematics #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1902.00710

openalex publication_date 2019/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we deal with the selection problem of flows of an irregular vector field. We first summarize an example from \citeCCS of a vector field b and a smooth approximation b_ε for which the sequence X^ε of flows of b_ε has subsequences converging to different flows of the limit vector field b. Furthermore, we give some heuristic ideas on the selection of a subclass of flows in our specific case.

Citations

• Continuity equations and ODE flows with non-smooth velocity

Related

• Rough flows
• On the commutativity of flows of rough vector fields
• Constructing general rough differential equations through flow approximations
• Path-dependent rough differential equations
• Flows driven by Banach space-valued rough paths