scholarly journals An Asymptotic Theory of Joint Sequential Changepoint Detection and Identification for General Stochastic Models

2021 ◽  
pp. 1-1
Author(s):  
Alexander G. Tartakovsky
Keyword(s):  
Stochastic Models ◽  
Asymptotic Theory ◽  
Changepoint Detection ◽  
Detection And Identification ◽  
General Stochastic

scholarly journals A fluid limit for a cache algorithm with general request processes

2010 ◽  
Vol 42 (03) ◽  
pp. 816-833 ◽  
Author(s):  
Takayuki Osogami
Keyword(s):  
Stochastic Models ◽  
Point Processes ◽  
Original System ◽  
Poisson Processes ◽  
Fluid Limit ◽  
Average Probability ◽  
Inhomogeneous Poisson Processes ◽  
Formal Limit ◽  
Stochastic Point Processes ◽  
General Stochastic

We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

scholarly journals A fluid limit for a cache algorithm with general request processes

2010 ◽  
Vol 42 (3) ◽  
pp. 816-833 ◽  
Author(s):  
Takayuki Osogami
Keyword(s):  
Stochastic Models ◽  
Point Processes ◽  
Original System ◽  
Poisson Processes ◽  
Fluid Limit ◽  
Average Probability ◽  
Inhomogeneous Poisson Processes ◽  
Formal Limit ◽  
Stochastic Point Processes ◽  
General Stochastic

We introduce a formal limit, which we refer to as a fluid limit, of scaled stochastic models for a cache managed with the least-recently-used algorithm when requests are issued according to general stochastic point processes. We define our fluid limit as a superposition of dependent replications of the original system with smaller item sizes when the number of replications approaches ∞. We derive the average probability that a requested item is not in a cache (average miss probability) in the fluid limit. We show that, when requests follow inhomogeneous Poisson processes, the average miss probability in the fluid limit closely approximates that in the original system. Also, we compare the asymptotic characteristics, as the cache size approaches ∞, of the average miss probability in the fluid limit to those in the original system.

scholarly journals Detection and identification of changes of hidden Markov chains: asymptotic theory

2021 ◽  
Author(s):  
Savas Dayanik ◽  
Kazutoshi Yamazaki
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Asymptotic Theory ◽  
Hidden Markov ◽  
Asymptotic Optimality ◽  
Sufficient Conditions ◽  
Change Point Detection ◽  
Unified Framework ◽  
Hidden Markov Chains ◽  
Detection And Identification

AbstractThis paper revisits a unified framework of sequential change-point detection and hypothesis testing modeled using hidden Markov chains and develops its asymptotic theory. Given a sequence of observations whose distributions are dependent on a hidden Markov chain, the objective is to quickly detect critical events, modeled by the first time the Markov chain leaves a specific set of states, and to accurately identify the class of states that the Markov chain enters. We propose computationally tractable sequential detection and identification strategies and obtain sufficient conditions for the asymptotic optimality in two Bayesian formulations. Numerical examples are provided to confirm the asymptotic optimality.

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