Abstract
This thesis is about stochastic integration with respect to Gaussian processes that are notsemimartingales. Firstly, we study approximations of integrals with respect to fractionalBrownian motion and derive an upper bound for an average approximation error. Secondly, westudy the existence of pathwise integrals with respect to a wide class of Gaussian processes andintegrands. We prove the existence of two different notions of pathwise integrals. Moreover,these two different integrals coincide. As an application of these results, the thesis containsintegral representations for arbitrary random variables. Finally, we study a certain modelinvolving a Gaussian process and provide estimators for different parameters. We applyMalliavin calculus and divergence integrals to obtain central limit theorems for our estimators.
Translated title of the contribution | Integrointi normaalissa maailmassa: fraktionaalinen Brownin liike sekä laajennuksia |
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Original language | English |
Qualification | Doctor's degree |
Awarding Institution |
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Supervisors/Advisors |
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Publisher | |
Print ISBNs | 978-952-60-5548-0 |
Electronic ISBNs | 978-952-60-5549-7 |
Publication status | Published - 2014 |
MoE publication type | G5 Doctoral dissertation (article) |
Keywords
- Gaussian process
- fractional Brownian motion
- approximation error
- pathwise integrals
- integral representation
- parameter estimation
- divergence integrals