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To investigate the complex dynamics of a biological neuron that is subject tosmall random perturbations we can use stochastic neuron models. While manytechniques have already been developed to study properties of such models,especially the analysis of the (expected) first-passage time or (E)FPT remainsdifficult. In this thesis I apply the large deviation theory (LDT), which isalready well-established in physics and finance, to the problem of determiningthe EFPT of the mean-reverting Ornstein-Uhlenbeck (OU) process. The OU processinstantiates the Stochastic Leaky Integrate and Fire model and thus serves asan example of a biologically inspired mathematical neuron model. I deriveseveral classical results using much simpler mathematics than the originalpublications from neuroscience and I provide a few conceivable interpretationsand perspectives on these derivations. Using these results I explore somepossible applications for parameter estimation and I provide an additionalmathematical justification for using a Poisson process as a small-noiseapproximation of the full model. Finally I perform several simulations toverify these results and to reveal systematic biases of this estimator.

Large Deviation Theory for Parameter Estimation in Simple Neuron Models