一類隨機動態(tài)過程基于q階樹的多尺度建模方法
A qth-order Tree-based Method for Multiscale Modeling of Stochastic Dynamic Processes
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摘要: 利用多尺度隨機模型能建立處理問題有效并行算法的這一優(yōu)勢,提出一類隨機動態(tài)過程基于一般q階樹的多尺度建模方法。首先,利用Markov過程的條件獨立性給出一類過程基于q階樹的多尺度表示方法;其次,基于q階樹多尺度表示和具體實例推導(dǎo)出多尺度模型中的狀態(tài)轉(zhuǎn)移矩陣、擾動陣、初始狀態(tài)和相應(yīng)的協(xié)方差矩陣等的具體形式,為具有Markov統(tǒng)計特性的過程或信號建立起多尺度隨機模型,這將為有效地解決多源同類信息和多源異類信息的數(shù)據(jù)融合等實際問題提供了理論基礎(chǔ);最后,給出一類Gauss-Markov過程基于三階樹和五階樹多尺度表示的計算機仿真結(jié)果,進一步驗證建立模型的實用性和有效性。
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關(guān)鍵詞:
- 多尺度隨機模型; q階樹; Markov過程; 多尺度表示
Abstract: In this paper, by using the advantage of an extremely efficient and highly parallelizable algorithm deriving from the multiscaie stochastic model to deal with a lot of practical problem, a general qth-order tree-based method for multiscale modeling of stochastic dynamic processes is developed. Firstly, using the property of conditional independence of Markov processes, a qth-order tree-based method for multiscale representation of a class of process is presented. Secondly, the representation forms of the parameters in the model, such as the state transition matrix, the disturbance matrix, the initial state and the corresponding covariance are deduced by example in detail based on -
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