Rough paths for physicists

Abstract:

Rough path theory emerged in the 1990’s motivated by practical and conceptual questions.

The general context is that of controlled differential equations, for example

Test $dU_t = F(U_t)$

is a known property of a system, changing with time, and Ut is an unknown whose evolution is to be computed via the equation. The emphasis is on the regularity of Xt as a function of time, and its consequences on that of Ut, making the necessary assumptions on f.