Sufficient conditions for fast quasi-Monte Carlo convergence

✍ Scribed by A. Papageorgiou

• Book ID: 104347278
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 209 KB
• Volume: 19
• Category: Article
• ISSN: 0885-064X
• DOI: 10.1016/s0885-064x(02)00004-3

✦ Synopsis

We study the approximation of d-dimensional integrals. We present sufficient conditions for fast quasi-Monte Carlo convergence. They apply to isotropic and non-isotropic problems and, in particular, to a number of problems in computational finance. We show that the convergence rate of quasi-Monte Carlo is of order n À1þpflog ng À1=2 with pX0: This is a worst case result. Compared to the expected rate n À1=2 of Monte Carlo it shows the superiority of quasi-Monte Carlo.