## Some Large Deviation Results for Diffusion Processes

• 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.
• Einige Resultate über große Abweichungen von Diffusionsprozessen

Author: Jochen Voß urn:nbn:de:hbz:386-kluedo-17631 Heinrich von Weizsäcker Doctoral Thesis English 2004 2004 Technische Universität Kaiserslautern Technische Universität Kaiserslautern 2004/07/22 2004/08/09 Diffusionsprozess ; Große Abweichung ; Stochastische Differentialgleichung Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Fxx Limit theorems [See also 28Dxx, 60B12] / 60F10 Large deviations 60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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