Randomized Milstein algorithm for approximation of solutions of jump-diffusion SDEs

2022/12/01 by Paweł Przybyłowicz, Przybyłowicz, Paweł, Verena Schwarz +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Engineering · #60H10 #65C30 #68Q25 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2212.00411

openalex publication_date 2022/12/01 · openalex created_date 2022/12/13 · openalex updated_date 2026/07/28

Abstract

We investigate the error of the randomized Milstein algorithm for solving scalar jump-diffusion stochastic differential equations. We provide a complete error analysis under substantially weaker assumptions than known in the literature. In case the jump-commutativity condition is satisfied, we prove optimality of the randomized Milstein algorithm by proving a matching lower bound. Moreover, we give some insight into the multidimensional case by investigating the optimal convergence rate for the approximation of jump-diffusion type Lévys' areas. Finally, we report numerical experiments that support our theoretical findings.

Cited by

• Randomised Euler-Maruyama Method for SDEs with Hölder Continuous Drift Coefficient Driven by α-stable Lévy Process

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