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For linear-cost-adjusted and geometric-discounted infinite sequences of i.i.d. random variables, point process convergence results are proved as the cost or discounting effect diminishes. These process convergence results are combined with continuous-mapping principles to obtain results on joint convergence of suprema and threshold-stopped random variables, and last-exit times and locations. Applications are made to several classical optimal stopping problems in these settings.

The extremal types theorem identifies asymptotic behaviour for the maxima of sequences of i.i.d. random variables. A parallel theorem is given which identifies the asymptotic behaviour of sequences of threshold-stopped random variables. Three new types of limit distributions arise, but normalizing constants remain the same as in the maxima case. Limiting joint distributions are also given for maxima and threshold-stopped random variables. Applications to the optimal stopping of i.i.d. random variables are given.

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Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

Limit theorems for threshold-stopped random variables with applications to optimal stopping

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2 results

Limit theorems for suprema, threshold-stopped random variables and last exits of i.i.d. random variables with costs and discounting, with applications to optimal stopping

Limit theorems for threshold-stopped random variables with applications to optimal stopping