The Existence of Solutions for Rough Differential Equations

In one of the last Saint Flour lectures in 2004, T. Lyons remarked that a Peano theorem for rough differential equations had not yet been proved. The first successful attempt to prove this existence result was carried out by A.M. Davie. Using generalized Euler schemes, Davie showed that when working in finite dimensions, differential equations driven by geometric p-rough paths, for 1 ~ p p) of a sequence of C~+c functions which satisfy an appropriate ellipticity condition, then the rough path solution of the equation can be defined as the almost sure limit in the p-variation metric of a sequence of solutions of stochastic differential equations.EThOS - Electronic Theses Online ServiceGBUnited Kingdo