In this article we explore the large deviation principle and its application in various mathematical and probabilistic contexts. Key results related to compactness and initial conditions for self-interacting diffusion are addressed, as well as the exit time problem in these processes.
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The article presents a generalization of assumptions A-1 and A-2, necessary to guarantee the existence and uniqueness of self-interacting diffusion in different scenarios. The implications of Kramers' theorem and results on exit location under these new assumptions are also discussed.
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