Some results associated with random walksTools Deligiannidis, Georgios (2010) Some results associated with random walks. PhD thesis, University of Nottingham.
AbstractIn this thesis we treat three problems from the theory and applications of random walks. The first question we tackle is from the theory of the optimal stopping of random walks. We solve the infinitehorizon optimal stopping problem for a class of reward functions admitting a representation introduced in Boyarchenko and Levendorskii [1], and obtain closed expressions for the expected reward and optimal stopping time. Our methodology is a generalization of an early paper by Darling et al. [2] and is based on probabilistic techniques: in particular a path decomposition related to the WienerHopf factorization. Examples from the literature and perturbations are treated to demonstrate the flexibility of our approach.
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