13 citations · 63 across the 22 of their papers we have counts for
25 papers
Optimal Tail Estimates for Differential Equations Driven by Fractional Brownian Motion
Horatio Boedihardjo, Xi Geng, Sheng Wang
The goal of the present paper is to investigate the exact decay rate of the tail probability for large , where is the solution to a multidimensio…
Statistical Inference for Fractional Diffusions
Pablo Ramses Alonso-Martin, Horatio Boedihardjo, Anastasia Papavasiliou
This is a review of statistical inference methodology for stochastic differential equations driven by fractional Brownian motion, otherwise called fractional diffusions. The first…
Cartan's Path Development, the Logarithmic Signature and a Conjecture of Lyons-Sidorova
Horatio Boedihardjo, Xi Geng, Sheng Wang
The signature transform, which is defined in terms of iterated path integrals of all orders, provides a faithful representation of the group of tree-reduced geometric rough paths.…
Statistical Inference for the Rough Homogenization Limit of Multiscale Fractional Ornstein-Uhlenbeck Processes
Pablo Ramses Alonso-Martin, Horatio Boedihardjo, Anastasia Papavasiliou
We study the problem of parameter estimation for the homogenization limit of multiscale systems involving fractional dynamics. In the case of stochastic multiscale systems driven b…
A representation for the Expected Signature of Brownian motion up to the first exit time of the planar unit disc
Horatio Boedihardjo, Lin He, Lisa Wang
The signature of a sample path is a formal series of iterated integrals along the path. The expected signature of a stochastic process gives a summary of the process that is especi…
On the Lack of Gaussian Tail for Rough Line Integrals along Fractional Brownian Paths
Horatio Boedihardjo, Xi Geng
We show that the tail probability of the rough line integral , where is a 2D fractional Brownian motion with Hurst parameter and…
Lipschitz-stability of Controlled Rough Paths and Rough Differential Equations
Horatio Boedihardjo, Xi Geng
We provide an account for the existence and uniqueness of solutions to rough differential equations under the framework of controlled rough paths. The case when the driving path is…
SL_2(R)-developments and Signature Asymptotics for Planar Paths with Bounded Variation
Horatio Boedihardjo, Xi Geng
The signature transform, defined by the formal tensor series of global iterated path integrals, is a homomorphism between the path space and the tensor algebra that has been studie…
The expected signature of Brownian motion stopped on the boundary of a circle has finite radius of convergence
Horatio Boedihardjo, Joscha Diehl, Marc Mezzarobba +1
The expected signature is an analogue of the Laplace transform for rough paths. Chevyrev and Lyons showed that, under certain moment conditions, the expected signature determines t…
Path Developments and Tail Asymptotics of Signature for Pure Rough Paths
Horatio Boedihardjo, Xi Geng, Nikolaos P. Souris
Solutions to linear controlled differential equations can be expressed in terms of iterated path integrals of the driving path. This collection of iterated integrals encodes essent…
A Non-vanishing Property for the Signature of a Path
Horatio Boedihardjo, Xi Geng
We prove that a continuous path with finite length in a real Banach space cannot have infinitely many zero components in its signature unless it is tree-like. In particular, this a…
An isomorphism between branched and geometric rough paths
Horatio Boedihardjo, Ilya Chevyrev
We exhibit an explicit natural isomorphism between spaces of branched and geometric rough paths. This provides a multi-level generalisation of the isomorphism of Lejay-Victoir (200…
Factorial Decay of Iterated Rough Integrals
Horatio Boedihardjo
In this complementary note to [1] (arXiv:1501.05641), we provide an alternative proof for the factorial decay estimate of iterated integrals for geometric rough paths without using…
The Tail Asymptotics of the Brownian Signature
Horatio Boedihardjo, Xi Geng
The signature of a path γis a sequence whose n-th term is the order-n iterated integrals of γ. It arises from solving multidimensional linear differential equations driven by γ. We…
A Quasi-sure Non-degeneracy Property for the Brownian Rough Path
Horatio Boedihardjo, Xi Geng, Xuan Liu +1
In the present paper, we are going to show that outside a slim set in the sense of Malliavin (or quasi-surely), the signature path (which consists of iterated path integrals in eve…
Note on the Signatures of Rough Paths in a Banach Space
Horatio Boedihardjo, Xi Geng, Terry Lyons +1
We prove some results, which are used in arXiv:1406.7871, about weakly geometric rough paths that are well-known in finite dimensions, but need proof in the infinite dimensional se…
Uniform Factorial Decay Estimate for the Remainder of Rough Taylor Expansion
Horatio Boedihardjo, Danyu Yang, Terry Lyons
We establish an uniform factorial decay estimate for the Taylor approximation of solutions to controlled differential equations. Its proof requires a factorial decay estimate for c…
Decay Rate of Iterated Integrals of Branched Rough Paths
Horatio Boedihardjo
Iterated integrals of paths arise frequently in the study of the Taylor's expansion for controlled differential equations. We will prove a factorial decay estimate, conjectured by…
The Signature of a Rough Path: Uniqueness
Horatio Boedihardjo, Xi Geng, Terry Lyons +1
In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation pat…
The Uniqueness of Signature Problem in the Non-Markov Setting
Horatio Boedihardjo, Xi Geng
The goal of this paper is to simplify and strengthen the Le Jan-Qian approximation scheme of studying the uniqueness of signature problem to the non-Markov setting. We establish a…
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…
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…