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

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Metadaten
Author:Jochen Voß
URN (permanent link):urn:nbn:de:hbz:386-kluedo-17631
Advisor:Heinrich von Weizsäcker
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2004
Year of Publication:2004
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2004/07/22
GND-Keyword:Diffusionsprozess ; Große Abweichung ; Stochastische Differentialgleichung
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):60F10 Large deviations
60H10 Stochastic ordinary differential equations [See also 34F05]

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