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Full Description
This book presents a selection of cutting-edge contributions from leading experts in the field, capturing the latest developments in stochastic analysis and its growing interface with neighboring disciplines. Stochastic analysis is a rapidly evolving branch of mathematics focused on the behavior of dynamical systems influenced by randomness. Over the past three decades, it has grown into one of the most vibrant and interdisciplinary areas of research, with profound impact on fields ranging from finance and physics to data science and engineering.
Topics include rough path theory, stochastic control, stochastic partial differential equations, random matrices, and applications in machine learning.
Building on the success of a recent international conference that brought together researchers from both academia and industry, this proceedings book highlights the depth and breadth of current work in the field. It serves as a valuable resource not only for academic researchers in mathematics, but also for practitioners working in areas such as quantitative finance, data-driven modeling, and applied probability.
Contents
Approximating the signature of Brownian motion for high order SDE simulation.- Randomisation of rough stochastic differential equations.- A Canonical Signature-Based Feature Set for Multivariate Time Series Classification.- Twin Brownian particle method for the study of Oberbeck-Boussinesq fluid flows.- Lower Bounds for the Support of Cubature Measures on Wiener Space and Optimal Degree-five Constructions.- Free Groups and Signatures.- A representation for the Expected Signature of Brownian motion up to the first exit time of the planar unit disc.- Asymptotic expansions of central limit distances in Vaserstein metrics.- A neural RDE-based model for solving path-dependent parabolic PDEs.- A Data-driven Market Simulator for Small Data Environments.- Mimicking and Conditional Control with Hard Killing.- Continuous random field solutions to parabolic SPDEs on p.c.f. fractals.- Pricing American options under rough volatility using signatures.- A new architecture of high-order deep neural networks that learn martingales.- Permutation recovery of spikes in noisy high-dimensional tensor estimation.- A User's Guide to KSig: GPU-Accelerated Computation of the Signature Kernel.
