Asymptotic Exponentiality of the Distribution of First Exit times for a Class of Markov Processes with Applications to Quickest Change Detection
نویسندگان
چکیده
We consider the first exit time of a nonnegative Harris-recurrent Markov process from the interval [0, A] as A → ∞. We provide an alternative method of proof of asymptotic exponentiality of the first exit time (suitably standardized) that does not rely on embedding in a regeneration process. We show that under certain conditions the moment generating function of a suitably standardized version of the first exit time converges to that ofExponential(1), and we connect between the standardizing constant and the quasi-stationary distribution (assuming it exists). The results are applied to the evaluation of a distribution of run length to false alarm in change-point detection problems.
منابع مشابه
Asymptotic Exponentiality of First Exit Times for Recurrent Markov Processes and Applications to Changepoint Detection
We study asymptotic properties (as A →∞) of the first exit time from the interval [0, A] of a non-negative Harris-recurrent Markov process. It is shown that under certain fairly general conditions the limiting distribution of the suitably normalized first exit time is exponential E(1) and that the moment generating function converges to that of E(1). The method of proof is based on considering ...
متن کاملAsymptotic Bayesian Theory of Quickest Change Detection for Hidden Markov Models
In the 1960s, Shiryaev developed a Bayesian theory of change-point detection in the i.i.d. case, which was generalized in the beginning of the 2000s by Tartakovsky and Veeravalli for general stochastic models assuming a certain stability of the log-likelihood ratio process. Hidden Markov models represent a wide class of stochastic processes that are very useful in a variety of applications. In ...
متن کاملA heuristic method for consumable resource allocation in multi-class dynamic PERT networks
This investigation presents a heuristic method for consumable resource allocation problem in multi-class dynamic Project Evaluation and Review Technique (PERT) networks, where new projects from different classes (types) arrive to system according to independent Poisson processes with different arrival rates. Each activity of any project is operated at a devoted service station located in a n...
متن کاملModeling land use changes using Markov chain model and LCM model
Land use maps are considered as the most important sources of information in natural resource management. The purpose of this research is to review, model, and predict landslide changes in the 30-year period by LCM model in Shiraz. In this research, TM Landsat 4, 5 and OLI Landsat 8 images were used for 1985, 2000 and 2015 respectively, as well as topographic maps and area coverage. Subsequent ...
متن کامل