A Tail-Respecting Explicit Numerical Scheme for Lévy-Driven SDEs With Superlinear Drifts (Ilya Pavlyukevich, Friedrich Schiller University Jena, Germany )

13.05.2025 10:30

We present an explicit numerical approximation scheme for the effective simulation of solutions to a multivariate stochastic differential
equation (SDE) with a superlinearly growing dissipative drift, driven by a multiplicative heavy-tailed Lévy process. The scheme combines the well-known Euler method with a Lie-Trotter-type splitting technique. The specific ordering of the splitting terms enables the approximation to capture all finite moments of the true solution. In the special case of SDEs driven solely by Brownian motion, our numerical scheme preserves the solution's superexponential moments. We prove strong convergence of approximations and determine the order of convergence.

This talk is based on the joint work with O. Aryasova (Jena) and O.
Kulyk (Wroclaw), arXiv:2504.07255 [math.PR]

Lieu

Conseil Général 7-9, Room 6-11, Séminaire d'analyse numérique (UNUSUAL TIME AND PLACE!)

entrée libre