165 citations · 1.6k across the 96 of their papers we have counts for
24 papers · 1 filter
A PDE approach for solving the characteristic function of the generalised signature process
Terry Lyons, Hao Ni, Jiajie Tao
The signature of a path, as a fundamental object in Rough path theory, serves as a generating function for non-commutative monomials on path space. It transforms the path into a gr…
Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach
Blanka Horvath, Maud Lemercier, Chong Liu +2
Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notio…
Hypercontractivity Meets Random Convex Hulls: Analysis of Randomized Multivariate Cubatures
Satoshi Hayakawa, Harald Oberhauser, Terry Lyons
Given a probability measure on a set and a vector-valued function , a common problem is to construct a discrete probability measure on such that…
General Signature Kernels
Thomas Cass, Terry Lyons, Xingcheng Xu
Suppose that and are two continuous bounded variation paths which take values in a finite-dimensional inner product space . Recent papers have introduced the truncated a…
Estimating the probability that a given vector is in the convex hull of a random sample
Satoshi Hayakawa, Terry Lyons, Harald Oberhauser
For a -dimensional random vector , let be the probability that the convex hull of independent copies of contains a given point . We provide several s…
Continuity in in theory using a constructive method and Rough Path Theory
Dmitry Beliaev, Terry J. Lyons, Vlad Margarint
Questions regarding the continuity in of the traces and maps appear very naturally in the study of SLE. In order to study the first question, we consider a natural coup…