Rough Paths above Weierstrass Functions - Cellarosi, Francesco; Selk, Zachary (Comptes Rendus. Mathématique)
Rough paths theory allows for a pathwise theory of solutions to differential equations driven by highly irregular signals. The fundamental observation of rough paths theory is that if one can define “iterated integrals” above a signal, then one can construct solutions to differential equations driven by the signal.The typical examples of the signals of interest are stochastic processes such as (fractional) Brownian motion. However, rough paths theory is not inherently random and therefore can treat irregular deterministic driving signals such as a (vector-valued) Weierstrass function. This note supplies a construction of a rough path above vector-valued Weierstrass functions.