15 citations · 56 across the 22 of their papers we have counts for
4 papers · 1 filter
Simple Piecewise Geodesic Interpolation of Simple and Jordan Curves with Applications
Horatio Boedihardjo, Xi Geng
We explicitly construct simple, piecewise minimizing geodesic, arbitrarily fine interpolation of simple and Jordan curves on a Riemannian manifold. In particular, a finite sequence…
Quasi-sure Existence of Gaussian Rough Paths and Large Deviation Principles for Capacities
Horatio Boedihardjo, Xi Geng, Zhongmin Qian
We construct a quasi-sure version (in the sense of Malliavin) of geometric rough paths associated with a Gaussian process with long-time memory. As an application we establish a la…
G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion
Xi Geng, Zhongmin Qian, Danyu Yang
The present paper is devoted to the study of sample paths of G-Brownian motion and stochastic differential equations (SDEs) driven by G-Brownian motion from the view of rough path…
On an Inversion Theorem for Stratonovich's Signatures of Multidimensional Diffusion Paths
Xi Geng, Zhongmin Qian
In the present paper, we prove that with probability one, the Stratonovich signatures of a multidimensional diffusion process (possibly degenerate) over [0,1], which is the collect…