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Start Over Creator Gordienko, Evgueni

1. Asymptotic properties and optimization of some non-Markovian stochastic processes

Creator:
Gordienko, Evgueni, Garcia, Antonio, and Ruiz de Chavez, Juan
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
nonmarkovian control sequence, average cost, attracting point, nonlinear optimization, and stability
Language:
English
Description:
We study the limit behavior of certain classes of dependent random sequences (processes) which do not possess the Markov property. Assuming these processes depend on a control parameter we show that the optimization of the control can be reduced to a problem of nonlinear optimization. Under certain hypotheses we establish the stability of such optimization problems.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Stability estimating in optimal sequential hypotheses testing

Creator:
Gordienko, Evgueni, Novikov, Andrey, and Zaitseva, Elena
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
sequential hypotheses test, simple hypothesis, optimal stopping, sequential probability ratio test, likehood ratio statistic, and stability inequality
Language:
English
Description:
We study the stability of the classical optimal sequential probability ratio test based on independent identically distributed observations X1,X2,… when testing two simple hypotheses about their common density f: f=f0 versus f=f1. As a functional to be minimized, it is used a weighted sum of the average (under f0) 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 X1,X2,… with the density f0. For τ∗ being the corresponding optimal stopping time we consider a situation when this rule is applied for testing between f0 and an alternative f~1, where f~1 is some approximation to f1. An inequality is obtained which gives an upper bound for the expected cost excess, when τ∗ is used instead of the rule τ~∗ optimal for the pair (f0,f~1). The inequality found also estimates the difference between the minimal expected costs for optimal tests corresponding to the pairs (f0,f1) and (f0,f~1).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public