Some Limit Theorems of Delayed Averages for Countable Nonhomogeneous Markov Chains

Zhong, Pingping; Yang, Weiguo; Shi, Zhiyan; Zhang, Yan

doi:10.1017/s0269964819000354

Cited by 1 publication

(1 citation statement)

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“…e Markov process refers to the division of a system into several small systems with different states, and each state can be transferred to another corresponding state according to its inherent transition probability. It is concluded that the Markov chain represents a process between one state and another, and that the probability of this process depends only on the corresponding preceding and following states [26]; its basic definition is as follows: let the random variable in discrete space I � (Xn, n ≥ 0), if any random variable n and any state i 0 , i 1 , i 2, i 3…”

Section: Markov Chainmentioning

confidence: 99%

The Offset Azimuth Prediction of Light Buoy Based on Markov Chain Optimization Multiplicative Seasonal Model

Ren

Zhou

et al. 2022

Mathematical Problems in Engineering

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Aimed at the problem of the large error caused by uncertain factors in the fitting process of the traditional multiplicative seasonal model, the advantages of the Markov chain in this study are applied to the multiplicative seasonal model to optimize the prediction results. Based on the residual value between the theoretical and actual values, the values of different intervals are divided into states. The transition probability matrix is established through different probabilities; then, the weighted sum of different prediction probabilities is carried out to select the optimal prediction state. The real number of Meizhou Bay portlight buoys is used to verify the prediction effect of the model, and MAE, MAPE, RMSE, RRMSE, SSE, R2 are used to calculate the error between the predicted value and the actual value. The results show that compared to the traditional multiplicative seasonal model and other prediction models, the prediction MAE of the MC-SARIMA model is decreased by 2.19003794, the MAPE is decreased by 0.66%, the RMSE is decreased by 2.092671823, the RRMSE is decreased by 0.006221352, the SSE is decreased by 404.0231931, and the R2 is increased by 0.224686247. It shows that the multiplicative seasonal model optimized by the Markov chain can predict the azimuth data of the light buoy more effectively than the traditional multiplicative seasonal model and other prediction models.

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Section: Markov Chainmentioning

confidence: 99%