When is a Markov chain regenerative?
نویسندگان
چکیده
A sequence of random variables {Xn}n≥0 is called regenerative if it can be broken up into iid components. The problem addressed in this paper is to determine under what conditions is a Markov chain regenerative. It is shown that an irreducible Markov chain with a countable state space is regenerative for any initial distribution if and only if it is recurrent (null or positive). An extension of this to the general state space case is also discussed.
منابع مشابه
Development of Markov Chain Grey Regression Model to Forecast the Annual Natural Gas Consumption
Accurate forecasting of annual gas consumption of the country plays an important role in energy supply strategies and policy making in this area. Markov chain grey regression model is considered to be a superior model for analyzing and forecasting annual gas consumption. This model Markov is a combination of the Markov chain and grey regression models. According to this model, the residual er...
متن کاملAbsorbing Markov Chain Models to Determine Optimum Process Target Levels in Production Systems with Rework and Scrapping
In this paper, absorbing Markov chain models are developed to determine the optimum process mean levels for both a single-stage and a serial two-stage production system in which items are inspected for conformity with their specification limits. When the value of the quality characteristic of an item falls below a lower limit, the item is scrapped. If it falls above an upper limit, the item is ...
متن کاملUsing Markov Chain to Analyze Production Lines Systems with Layout Constraints
There are some problems with estimating the time required for the manufacturing process of products, especially when there is a variable serving time, like control stage. These problems will cause overestimation of process time. Layout constraints, reworking constraints and inflexible product schedule in multi product lines need a precise planning to reduce volume in particular situation of lin...
متن کاملOptimal Control of Markov Regenerative Processes
In the paper the integration of available results on SemiMarkov Decision Processes and on Markov Regenerative Processes is attempted, in order to de ne the mathematical framework for solving decision problems where the underlying structure state process is a Markov Regenerative Process, referred to as Markov Regenerative Decision Process. The essential question investigated here is which descri...
متن کاملTaylor Expansion for the Entropy Rate of Hidden Markov Chains
We study the entropy rate of a hidden Markov process, defined by observing the output of a symmetric channel whose input is a first order Markov process. Although this definition is very simple, obtaining the exact amount of entropy rate in calculation is an open problem. We introduce some probability matrices based on Markov chain's and channel's parameters. Then, we try to obtain an estimate ...
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 2013