本文選題：Markov鏈 + 隨機(jī)映射�。� 參考：《中國科學(xué):數(shù)學(xué)》2017年12期

【摘要】：復(fù)雜系統(tǒng)與過程的數(shù)學(xué)建模需要用隨機(jī)動力學(xué)(stochastic dynamics)的思想和方法.隨機(jī)動力學(xué)的理論有著兩種不同的數(shù)學(xué)表述:隨機(jī)過程(stochastic processes)和隨機(jī)動力系統(tǒng)(random dynamical systems).后者是比前者更為精細(xì)的數(shù)學(xué)模型,它不但給出對應(yīng)于每一個初值的隨機(jī)過程,還全面地描述不同初值的多條隨機(jī)軌道如何同時隨時間變化.前者恰恰表述了有內(nèi)在隨機(jī)性的個體的運(yùn)動,而后者則反映了多個相同的確定性個體同時經(jīng)歷同一個隨機(jī)環(huán)境.本文稱這兩種情形為內(nèi)源噪聲和外源噪聲.兩者都在化學(xué)和生物學(xué)中有廣泛的應(yīng)用.近年來興起的以圖G(V,E)為基礎(chǔ)的概率布爾網(wǎng)絡(luò)正是一類以{0,1}~V為狀態(tài)空間的隨機(jī)動力系統(tǒng)(RDS).本文介紹有關(guān)離散時間離散空間的RDS,同時也給出一個它在統(tǒng)計(jì)推斷隱Markov模型的收斂速率估算中的應(yīng)用.
[Abstract]:The mathematical modeling of complex systems and processes requires the idea and method of stochastic dynamics.The theory of stochastic dynamics has two different mathematical expressions: stochastic processes and random dynamical systems.The latter is a more precise mathematical model than the former. It not only gives a stochastic process corresponding to each initial value, but also describes how multiple random orbits with different initial values change simultaneously with time.The former precisely describes the movement of individuals with inherent randomness, while the latter reflects the fact that multiple identical deterministic individuals experience the same random environment at the same time.In this paper, we call these two cases endogenous noise and exogenous noise.Both are widely used in chemistry and biology.The probabilistic Boolean network, which is based on the graph Geng V (E) in recent years, is a kind of random dynamic system with {0 ~ 1} V as the state space.In this paper, we introduce the RDSs of discrete time discrete space, and give an application of RDS in the estimation of convergence rate of statistical inferred implicit Markov model.
【作者單位】： Department
【分類號】：O19
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本文編號：1738664