Related papers: A PDE approach for solving the characteristic func…

A central question in rough path theory is characterising the law of stochastic processes on path spaces. It is established in [I. Chevyrev & T. Lyons, Characteristic functions of measures on geometric rough paths, Ann. Probab. 44 (2016),…

The signature of a path provides a top down description of the path in terms of its effects as a control [Differential Equations Driven by Rough Paths (2007) Springer]. The signature transforms a path into a group-like element in the tensor…

The signature is a collection of iterated integrals describing the "shape" of a path. It appears naturally in the Taylor expansions of controlled differential equations and, as a consequence, is arguably the central object within rough path…

We define a characteristic function for probability measures on the signatures of geometric rough paths. We determine sufficient conditions under which a random variable is uniquely determined by its expected signature, thus partially…

The expected signature kernel arises in statistical learning tasks as a similarity measure of probability measures on path space. Computing this kernel for known classes of stochastic processes is an important problem that, in particular,…

We establish a universal approximation theorem for signatures of rough paths that are not necessarily weakly geometric. By extending the path with time and its rough path bracket terms, we prove that linear functionals of the signature of…

We develop a consistent method for estimating the parameters of a rich class of path-dependent SDEs, called signature SDEs, which can model general path-dependent phenomena. Path signatures are iterated integrals of a given path with the…

Signature stochastic differential equations (SDEs) constitute a large class of stochastic processes, here driven by Brownian motions, whose characteristics are linear maps of their own signature, i.e. of iterated integrals of the process…

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 especially useful for studying stochastic differential equations…

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 general framework for a class of multidimensional stochastic…

Path signatures are powerful nonparametric tools for time series analysis, shown to form a universal and characteristic feature map for Euclidean valued time series data. We lift the theory of path signatures to the setting of Lie group…

The signature of a path is a sequence, whose $n$-th term contains $n$-th order iterated integrals of the path. These iterated integrals of sample paths of stochastic processes arise naturally when studying solutions of differential equation…

The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…

Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effective way to capture sequentially ordered information,…

We consider the orthogonalisation of the signature of a stochastic process as the analogue of orthogonal polynomials on path-space. Under an infinite radius of convergence assumption, we prove density of linear functions on the signature in…

In stochastic analysis, a standard method to study a path is to work with its signature. This is a sequence of tensors of different order that encode information of the path in a compact form. When the path varies, such signatures…

The signature of a path is an essential object in the theory of rough paths. The signature representation of the data stream can recover standard statistics, e.g. the moments of the data stream. The classification of random walks indicates…

Physical Brownian motion describes the dynamics of a Brownian particle experiencing frictional force. It was investigated in the classical work [L. S. Ornstein and G. E. Uhlenbeck, Phys. Rev. 36 (1930)] as a physically meaningful approach…

Randomised signature has been proposed as a flexible and easily implementable alternative to the well-established path signature. In this article, we employ randomised signature to introduce a generative model for financial time series data…

In the last decade, the concept of path signature has achieved significant success in data science applications. It offers a powerful set of features that effectively capture and describe the characteristics of paths or sequential data.…