Perturbation bounds and degree of imprecision for uniquely convergent imprecise Markov chains
نویسنده
چکیده
The effect of perturbations of parameters for uniquely convergent imprecise Markov chains is studied. We provide the maximal distance between the distributions of original and perturbed chain and maximal degree of imprecision, given the imprecision of the initial distribution. The bounds on the errors and degrees of imprecision are found for the distributions at finite time steps, and for the stationary distributions as well.
منابع مشابه
Stochastic bounds for a single server queue with general retrial times
We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds. The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques.
متن کاملStrong Stability and Perturbation Bounds for Discrete Markov Chains
We consider the stability problem of discrete Markov chains when their transition matrices are perturbed. For finite irreducible Markov chains many perturbation bounds for the stationary vector are available. In this paper, we identify a condition under which these bounds are carried over to discrete irreducible Markov chains which are not finite.
متن کاملPerturbation Analysis in Verification of Discrete-Time Markov Chains
Perturbation analysis in probabilistic verification addresses the robustness and sensitivity problem for verification of stochastic models against qualitative and quantitative properties. We identify two types of perturbation bounds, namely non-asymptotic bounds and asymptotic bounds. Non-asymptotic bounds are exact, pointwise bounds that quantify the upper and lower bounds of the verification ...
متن کاملImprecise Continuous-Time Markov Chains: Efficient Computational Methods with Guaranteed Error Bounds
Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential equation. As there is no general analytical expression for this solution, efficient numerical approximation methods are essential to the applicability of this mode...
متن کاملUsing Imprecise Continuous Time Markov Chains for Assessing the Reliability of Power Networks with Common Cause Failure and Non-Immediate Repair
We explore how imprecise continuous time Markov chains can improve traditional reliability models based on precise continuous time Markov chains. Specifically, we analyse the reliability of power networks under very weak statistical assumptions, explicitly accounting for non-stationary failure and repair rates and the limited accuracy by which common cause failure rates can be estimated. Bounds...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2016