Curvilinear integrals along enriched paths. (English) Zbl 1110.60031

Feyel, Denis; de La Pradelle, Arnaud

Electron. J. Probab. 11, Paper No. 34, 860-892 (2006).

Summary: Inspired by the fundamental work of T. J. Lyons, we develop a theory of curvilinear integrals along a new kind of enriched paths in \(\mathbb{R}^d\). We apply these methods to the fractional Brownian motion, and prove a support theorem for SDE driven by the Skorokhod fBM of Hurst parameter \(H>1/4\).

MSC:

60G15	Gaussian processes
26B20	Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
26B35	Special properties of functions of several variables, Hölder conditions, etc.
60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)