13 citations · 63 across the 22 of their papers we have counts for
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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.…
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…
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…
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…
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…
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 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…
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…
Quasi-sure convergence theorem in -variation distance for stochastic differential equations
H. Boedihardjo, Z. Qian
In this paper by calculating carefully the capacities (defined by high order Sobolev norms on the Wiener space) for some functions of Brownian motion, we show that the dyadic appro…