On numerical integration by the shift and application to Wiener space

✍ Scribed by Nicolas Bouleau

• Publisher: Springer Netherlands
• Year: 1991
• Tongue: English
• Weight: 675 KB
• Volume: 25
• Category: Article
• ISSN: 0167-8019
• DOI: 10.1007/bf00047003

✦ Synopsis

Since the advantages of quasi-Monte Carlo methods vanish when the dimension of the basic space increases, the question arises whether there are better methods than the classical Monte Carlo in large or infinite-dimensional basic spaces. We study here the use of the shift operator with the pointwise ergodic theorem whose implementation is particularly interesting. After recalling the theoretical results on the speed of convergence in a form useful for applications, we give sufficient criteria for the law of iterated logarithm in several cases and, in particular, in situations involving the Wiener space.