A higher order approximation method for jump-diffusion SDEs with discontinuous drift coefficient

Przybyłowicz, Paweł; Schwarz, Verena; Szölgyenyi, Michaela

doi:10.48550/arxiv.2211.08739

Cited by 1 publication

(1 citation statement)

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“…In paper [31], the authors analyzed a compensated projected EM method for stochastic differential equations with jumps under specific assumptions that admit the superlinearity of the jump and diffusion coefficients. A higher order approximation for jump diffusion SDEJs with discontinuous drifts has been stated in [32]. Additionally, a new simplified weak second-order scheme for solving SDEJs was established in [33].…”

Section: Numerical Approximationsmentioning

confidence: 99%

Numerical Solutions of Stochastic Differential Equations with Jumps and Measurable Drifts

Siddiqui,

Eddahbi,

Kebiri

2023

Mathematics

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This paper deals with numerical analysis of solutions to stochastic differential equations with jumps (SDEJs) with measurable drifts that may have quadratic growth. The main tool used is the Zvonkin space transformation to eliminate the singular part of the drift. More precisely, the idea is to transform the original SDEJs to standard SDEJs without singularity by using a deterministic real-valued function that satisfies a second-order differential equation. The Euler–Maruyama scheme is used to approximate the solution to the equations. It is shown that the rate of convergence is 12. Numerically, two different methods are used to approximate solutions for this class of SDEJs. The first method is the direct approximation of the original equation using the Euler–Maruyama scheme with specific tests for the evaluation of the singular part at simulated values of the solution. The second method consists of taking the inverse of the Euler–Maruyama approximation for Zvonkin’s transformed SDEJ, which is free of singular terms. Comparative analysis of the two numerical methods is carried out. Theoretical results are illustrated and proved by means of an example.

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Section: Numerical Approximationsmentioning

confidence: 99%