Some results associated with random walks
Deligiannidis, Georgios (2010) Some results associated with random walks. PhD thesis, University of Nottingham.
In 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 infinite-horizon optimal stopping problem for a class of reward functions admitting a representation introduced in Boyarchenko and Levendorskii , 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.  and is based on probabilistic techniques: in particular a path decomposition related to the Wiener-Hopf factorization. Examples from the literature and perturbations are treated to demonstrate the flexibility of our approach.
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