Mathematicians from the Universities of Luxembourg, Aarhus and Tokyo have recently published their findings in the renowned journal Annals of Applied Probability. In this paper, they demonstrate how probability theory provides a better understanding of numerical simulation errors and could be useful for different applications.
The paper entitled “Edgeworth expansion for Euler approximation of continuous diffusion processes” has been published in one of the top journals in the field of probability, which focuses on modern applications of probability theory. Euler approximation is a classical numerical method for simulation of deterministic and stochastic differential equations. While the error analysis in the deterministic context are well understood, first articles on the limiting behaviour of Euler schemes in the stochastic framework appeared only in the late 90’s.
“Our manuscript goes beyond the first order limit theory for Euler schemes as we provide the next order term in the error analysis. The theoretical results help to provide a better understanding of strong and weak errors, and they find numerous applications in biology, physics and economics among other sciences”, comments Mark Podolskij, Professor of financial mathematics within the Department of Mathematics at the University of Luxembourg and one of the three authors of the paper.
Article “Edgeworth expansion for Euler approximation of continuous diffusion processes”, Annals of Applied Probability, 2020