On the Euler-Maruyama scheme for spectrally one-sided L\'evy driven SDEs with H\"older continuous coefficients

TL;DR

This paper analyzes the strong convergence rate of the Euler-Maruyama scheme for jump-driven SDEs with H"older continuous coefficients, extending results to models generalizing the CIR process with jumps.

Contribution

It establishes the strong convergence rate of the Euler-Maruyama scheme for spectrally one-sided Lévy-driven SDEs with H"older continuous coefficients, generalizing previous models.

Findings

Derived the strong convergence rate under similar assumptions as for strong existence.

Extended analysis to models generalizing the CIR process with jumps.

Confirmed pathwise uniqueness and strong existence for the studied equations.

Abstract

We study in this article the strong rate of convergence of the Euler-Maruyama scheme and associated with the jump-type equation introduced in Li and Mytnik. We obtain the strong rate of convergence under similar assumptions for strong existence and pathwise uniqueness. Models of this type can be considered as a generalization of the CIR (Cox-Ingersoll-Ross) process with jumps.