English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A new algorithm for the approximation and simulation of twofold iteratedstochastic integrals together with the corresponding L\'{e}vy areas driven by amultidimensional Brownian motion is proposed. The algorithm is based on atruncated Fourier series approach. However, the approximation of the remainderterms differs from the approach considered by Wiktrosson (2001). As the mainadvantage, the presented algorithm makes use of a diagonal covariance matrixfor the approximation of one part of the remainder term and has a higheraccuracy due to an exact approximation of the other part of the remainder. Thisresults in a significant reduction of the computational cost compared to, e.g.,the algorithm introduced by Wiktorsson. Convergence in $L^p(\Omega)$-norm with$p \geq 2$ for the approximations calculated with the new algorithm as well asfor approximations calculated by the basic truncated Fourier series algorithmis proved and the efficiency of the new algorithm is analyzed.

On the Approximation and Simulation of Iterated Stochastic Integrals and  the Corresponding L\'{e}vy Areas in Terms of a Multidimensional Brownian  Motion