Let M be the transition matrix, and the initial state distribution , for a discrete-time nite-state irreducible Markov chain. A stopping rule for M is an algorithm which observes the progress of the chain and then stops it at some random time ?; the distribution of the nal state is denoted by ?. We give a useful characterization for stopping rules which are optimal for given target distribution...

A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new stopping rule. Numerical experiments show that the proposed stopping rule is efficient. Equations with monotone operators are of interest in many application...

One of the key issues in symbolic dynamic filtering (SDF) is how to obtain a lower bound on the length of symbol blocks for computing the state probability vectors of probabilistic finite-state automata (PFSA). Having specified an absolute error bound at a confidence level, this short work formulates a stopping rule by making use of Markov chain Monte Carlo (MCMC) computations. © 2010 Elsevier ...

• A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version ...

In this paper, two-stage and purely sequential estimation procedures are considered to construct fixed-width confidence intervals for the reliability parameter under the stress-strength model when the stress and strength are independent exponential random variables with different scale parameters. The exact distribution of the stopping rule under the purely sequential procedure is approximated ...

Let X1,X2, . . . be and i.i.d. sequence. We consider three stopping rule problems for stopping the sequence of partial sums, Sn = ∑n 1 Xi, each of which has a timeinvariance for the payoff that allows us to describe the optimal stopping rule in a particularly simple form, depending on one or two parameters. For certain distributions of the Xn, the optimal rules are found explicitly. The three p...

Although people expect to improve by investing effort in solving a problem, several studies have found negative timeconfidence correlations in various problem-solving tasks. The present study employed the metacognitive approach to illuminate why, despite lengthy thinking, people provide solutions in which they have only low confidence. According to the proposed Diminishing Criterion Model (DCM)...