A weak limit theorem for numerical approximation of Brownian semi-stationary processes

Mark Podolskij, Nopporn Thamrongrat

Research output: Contribution to book/anthology/report/proceedingBook chapterResearchpeer-review

Abstract

In this paper we present a weak limit theorem for a numerical approximation of Brownian semi-stationary processes studied in [14]. In the original work of [14] the authors propose to use Fourier transformation to embed a given one dimensional (Lévy) Brownian semi-stationary process into a two-parameter stochastic field. For the latter they use a simple iteration procedure and study the strong approximation error of the resulting numerical scheme given that the volatility process is fully observed. In this work we present the corresponding weak limit theorem for the setting, where the volatility/drift process needs to be numerically simulated. In particular, weak approximation errors for smooth test functions can be obtained from our asymptotic theory.

Original languageEnglish
Title of host publicationStochastics of Environmental and Financial Economics
EditorsFred Espen Benth, Giulia Di Nunno
Number of pages19
PublisherSpringer
Publication date2016
Pages101-120
ISBN (Print)978-3-319-23424-3
ISBN (Electronic)978-3-319-23425-0
DOIs
Publication statusPublished - 2016
SeriesSpringer Proceedings in Mathematics & Statistics
Volume138
ISSN2194-1009

Keywords

  • Ambit fields
  • Brownian semi-stationary processes
  • Numerical schemes
  • Weak limit theorems

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