Displaying similar documents to “Differential equations driven by rough signals.”

Path-wise solutions of stochastic differential equations driven by Lévy processes.

David R. E. Williams (2001)

Revista Matemática Iberoamericana


In this paper we show that a path-wise solution to the following integral equation Yt = ∫0 t  f(Yt) dXt,     Y0 = a ∈ Rd, exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α >...

Rough paths via sewing Lemma

Laure Coutin (2012)

ESAIM: Probability and Statistics


We present the rough path theory introduced by Lyons, using the swewing lemma of Feyel and de Lapradelle.

Path differentiation: further unification

Udayan Darji, Michael Evans (1995)

Fundamenta Mathematicae


A. M. Bruckner, R. J. O'Malley, and B. S. Thomson introduced path differentiation as a vehicle for unifying the theory of numerous types of generalized differentiation of real valued functions of a real variable. Part of their classification scheme was based on intersection properties of the underlying path systems. Here, additional light is shed on the relationships between these various types of path differentiation and it is shown how composite differentiation and first return differentiation...