Joint Probability/Statistics and Math Finance Colloquium: A Kernel Framework for Linear Operator Equations

Valentin Tissot-Daguette, Bloomberg

Title: A Kernel Framework for Linear Operator Equations

Abstract: We present a Reproducing Kernel Hilbert Space (RKHS) framework for solving linear operator equations. By transferring the operator's action onto the kernel, these equations can be reduced to finite-dimensional ridge regressions. We also leverage random Nyström approximations to make implementations tractable while maintaining optimal convergence rates. Numerical experiments, notably on parabolic PIDEs, confirm the solver's accuracy and near-invariance to sample point selection. We conclude by constructing kernels on path spaces driven by transformer processes, paving the way for applications to path-dependent PDEs.

Based on joint works with Damir Filipović (EPFL) and Josef Teichmann (ETH Zurich).