An Improved Error Bound Theorem for Approximate Markov Chain s
نویسنده
چکیده
Recently an error bound theorem was reported to conclude analytic error bounds for approximate Markov chains. The theorem required a uniform bound for marginal expectations of the approximate model. This note will relax this bound to steady state rather than marginal expectations as of practical interest: (i) to simplify verification and/or (ii) to obtain a more accurate error bound. An ALOHA-type Communications example is studied to support the results.
منابع مشابه
The Rate of Rényi Entropy for Irreducible Markov Chains
In this paper, we obtain the Rényi entropy rate for irreducible-aperiodic Markov chains with countable state space, using the theory of countable nonnegative matrices. We also obtain the bound for the rate of Rényi entropy of an irreducible Markov chain. Finally, we show that the bound for the Rényi entropy rate is the Shannon entropy rate.
متن کاملQuantifying the accuracy of approximate diffusions and Markov chains
Markov chains and diffusion processes are indispensable tools in machine learning and statistics that are used for inference, sampling, and modeling. With the growth of large-scale datasets, the computational cost associated with simulating these stochastic processes can be considerable, and many algorithms have been proposed to approximate the underlying Markov chain or diffusion. A fundamenta...
متن کاملSERIE RESEHRCH mEmORBnDH APPROXIMATE UNIFORMIZATION FOR CONTINUOUS-TIME MARKOV CHAINS WITH AN APPLICATION TO PERFORMABILITY ANALYSIS
An approximate version of the Standard uniformization technique is introduced for application to continuous-time Markov chains with unbounded jump rates. This technique is shown to be asymptotically exact and an error bound for the order of its accuracy is provided. An illustrative queueing application is included.
متن کاملMarkov Chain Analogue Year Daily Rainfall Model and Pricing of Rainfall Derivatives
In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurrence and intensity model we obtain Markov Chain Analogue Year gamma model (MCAYGM), Markov Chain Analogue Year exponentia...
متن کاملLow and Upper Bound of Approximate Sequence for the Entropy Rate of Binary Hidden Markov Processes
In the paper, the approximate sequence for entropy of some binary hidden Markov models has been found to have two bound sequences, the low bound sequence and the upper bound sequence. The error bias of the approximate sequence is bound by a geometric sequence with a scale factor less than 1 which decreases quickly to zero. It helps to understand the convergence of entropy rate of generic hidden...
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 2007