23 citations · 99 across the 56 of their papers we have counts for
6 papers · 2 filters
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…
Backward Stochastic Differential Equations Associated with the Vorticity Equations
Ana Bela Cruzeiro, Zhongmin M. Qian
We derive a non-linear version of the Feynman-Kac formula for the solutions of the vorticity equation in dimension 2 with space periodic boundary conditions. We prove the existence…
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…
Expected signature of Gaussian processes with strictly regular kernels
H. Boedihardjo, A. Papavasiliou, Z. Qian
We compute the expected signature of a class of Gaussian processes which is a subclass of the Gaussian processes with regular kernels, in the sense of Alos, Mazet and Nualart.
Uniqueness of signature for simple curves
H. Boedihardjo, H. Ni, Z. Qian
We propose a topological approach to the problem of determining a curve from its iterated integrals. In particular, we prove that a family of terms in the signature series of a two…