Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augme...Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.展开更多
This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability...This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. The method was able to determine the block sizes b and probability p attached to its random selections. The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model.展开更多
This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random ...This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.展开更多
In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations....In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations. We establish laws of the iterated logarithm of theLipschitz-1/2 modulus of PL-process and cumulative hazard process. These results for the PL-processare sharper than other results found in the literature, which can be used to establish theasymptotic properties of many statistics.展开更多
Dear Editor,This letter investigates the optimal transmission scheduling problem in remote state estimation systems over an unknown wireless channel.We propose a partially observable Markov decision Process(POMDP)fram...Dear Editor,This letter investigates the optimal transmission scheduling problem in remote state estimation systems over an unknown wireless channel.We propose a partially observable Markov decision Process(POMDP)framework to model the sensor scheduling problem.By truncating and simplifying the POMDP problem,we have established the properties of the optimal solution under the POMDP model,through a fixed-point contraction method,and have shown that the threshold structure of the POMDP solution is not easily attainable.Subsequently,we obtained a suboptimal solution via Qlearning.Numerical simulations are used to demonstrate the efficacy of the proposed Q-learning approach.展开更多
文摘Let Q be the Q-matrix of an irreducible, positive recurrent Markov process on a countable state space. We show that, under a number of conditions, the stationary distributions of the n × n north-west corner augmentations of Q converge in total variation to the stationary distribution of the process. Two conditions guaranteeing such convergence include exponential ergodicity and stochastic monotonicity of the process. The same also holds for processes dominated by a stochastically monotone Markov process. In addition, we shall show that finite perturbations of stochastically monotone processes may be viewed as being dominated by a stochastically monotone process, thus extending the scope of these results to a larger class of processes. Consequently, the augmentation method provides an attractive, intuitive method for approximating the stationary distributions of a large class of Markov processes on countably infinite state spaces from a finite amount of known information.
文摘This paper introduced a bootstrap method called truncated geometric bootstrap method for time series stationary process. We estimate the parameters of a geometric distribution which has been truncated as a probability model for the bootstrap algorithm. This probability model was used in resampling blocks of random length, where the length of each blocks has a truncated geometric distribution. The method was able to determine the block sizes b and probability p attached to its random selections. The mean and variance were estimated for the truncated geometric distribution and the bootstrap algorithm developed based on the proposed probability model.
文摘This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.
文摘In this paper, we give a detailed description of the local behavior of theLipschitz-1/2 modulus for cumulative hazard process and PL-process when the data are subject to lefttruncation and right censored observations. We establish laws of the iterated logarithm of theLipschitz-1/2 modulus of PL-process and cumulative hazard process. These results for the PL-processare sharper than other results found in the literature, which can be used to establish theasymptotic properties of many statistics.
基金supported in part by the Frontier Technology R&D Plan of Jiangsu Province(BF2024065)the Shenzhen Science and Technology Program(JCYJ20230807114609019)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX22_0236).
文摘Dear Editor,This letter investigates the optimal transmission scheduling problem in remote state estimation systems over an unknown wireless channel.We propose a partially observable Markov decision Process(POMDP)framework to model the sensor scheduling problem.By truncating and simplifying the POMDP problem,we have established the properties of the optimal solution under the POMDP model,through a fixed-point contraction method,and have shown that the threshold structure of the POMDP solution is not easily attainable.Subsequently,we obtained a suboptimal solution via Qlearning.Numerical simulations are used to demonstrate the efficacy of the proposed Q-learning approach.
