Lower error bounds and optimality of approximation for jump-diffusion SDEs with discontinuous drift

Journal article

In this paper sharp lower error bounds for numerical methods for jump-diffusion stochastic differential equations (SDEs) with discontinuous drift are proven. The approximation of jump-diffusion SDEs with non-adaptive as well as jump-adapted approximation schemes is studied and lower error bounds of order 3/4 for both classes of approximation schemes are provided. This yields optimality of the transformation-based jump-adapted quasi-Milstein scheme.

Authors: Przybyłowicz, P; Schwarz, V; Szölgyenyi, M

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Springer
• Journal: BIT Numerical Mathematics
• Volume: 64
• Issue: 4
• Pages: 35-35
• Article number: 35
• Publication date: 2024-09-09
• Acceptance date: 2024-08-19
• DOI: 10.1007/s10543-024-01036-7
• EISSN: 1572-9125
• ISSN: 0006-3835
• Language: English
• Keywords: Stochastic differential equation; Mathematics; Transformation (genetics); Order (exchange); Mathematical analysis; Physics; Jump diffusion; Jump; Jump process; Diffusion; Approximation error; Applied mathematics