Path-Dependent SDEs: Solutions and Parameter Estimation

Date

Feb 12, 2026

Time

3:00 PM - 4:00 PM

Speaker

Pardis Semnani

Affiliation

University of British Columbia

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

In this talk, we discuss how temporal causal structures can be modelled using a path-dependent stochastic differential equation (SDE). We then consider a rich class of path-dependent SDEs, called signature SDEs, which can model general path-dependent phenomena. We provide conditions that ensure the existence and uniqueness of solutions to a general signature SDE. Path signatures are iterated integrals of a given path with the property that any sufficiently nice function of the path can be approximated by a linear functional of its signatures. This is why we model the drift and diffusion of our signature SDE as linear functions of path signatures, and then introduce the Expected Signature Matching Method (ESMM) for linear signature SDEs, which enables inference of the signature-dependent drift and diffusion coefficients from observed trajectories. Furthermore, we show that the ESMM is consistent: given sufficiently many samples and Picard iterations used by the method, the parameters estimated by the ESMM approach the true parameter with arbitrary precision. We discuss the asymptotic distribution of the estimator obtained from the ESMM, and finally, demonstrate on a variety of empirical simulations that our ESMM accurately infers the drift and diffusion parameters from observed trajectories. While parameter estimation is often restricted by the need for a suitable parametric model, this study makes progress toward a completely general framework for SDE parameter estimation, using signature terms to model arbitrary path-independent and path-dependent processes.This talk is based on joint work with Vincent Guan, Elina Robeva, and Darrick Lee.

Last modified: Feb 12, 2026, 7:36:39 AM