Some Large Deviation Results for Diffusion Processes

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Abstract

In this text we survey some large deviation results for diffusion processes. The first chapters present results from the literature such as the Freidlin-Wentzell theorem for diffusions with small noise. We use these results to prove a new large deviation theorem about diffusion processes with strong drift. This is the main result of the thesis. In the later chapters we give another application of large deviation results, namely to determine the exponential decay rate for the Bayes risk when separating two different processes. The final chapter presents techniques which help to experiment with rare events for diffusion processes by means of computer simulations.

Citations

I believe that this work is cited in the following texts. If you know of any more citations, please let me know.

• J. Voss: Upper and Lower Bounds in Exponential Tauberian Theorems. Tbilisi Mathematical Journal, vol. 2, pp. 41–50, 2009.
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• J. Voss: Large Deviations for One Dimensional Diffusions with a Strong Drift. Electronic Journal of Probability, vol. 13, no. 53, pp. 1479–1526, 2008.
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