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Stability estimating in optimal stopping problem

Elena Zaitseva — 2008

Kybernetika

We consider the optimal stopping problem for a discrete-time Markov process on a Borel state space X . It is supposed that an unknown transition probability p ( · | x ) , x X , is approximated by the transition probability p ˜ ( · | x ) , x X , and the stopping rule τ ˜ * , optimal for p ˜ , is applied to the process governed by p . We found an upper bound for the difference between the total expected cost, resulting when applying τ ˜ * , and the minimal total expected cost. The bound given is a constant times sup x X p ( · | x ) - p ˜ ( · | x ) , where · is the total variation...

About stability of risk-seeking optimal stopping

Raúl Montes-de-OcaElena Zaitseva — 2014

Kybernetika

We offer the quantitative estimation of stability of risk-sensitive cost optimization in the problem of optimal stopping of Markov chain on a Borel space X . It is supposed that the transition probability p ( · | x ) , x X is approximated by the transition probability p ˜ ( · | x ) , x X , and that the stopping rule f ˜ * , which is optimal for the process with the transition probability p ˜ is applied to the process with the transition probability p . We give an upper bound (expressed in term of the total variation distance: sup x X p ( · | x ) - p ˜ ( · | x ) ) for...

Stability estimating in optimal sequential hypotheses testing

We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X 1 , X 2 , when testing two simple hypotheses about their common density f : f = f 0 versus f = f 1 . As a functional to be minimized, it is used a weighted sum of the average (under f 0 ) sample number and the two types error probabilities. We prove that the problem is reduced to stopping time optimization for a ratio process generated by X 1 , X 2 , with the density f 0 . For τ * being the corresponding...

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