随机动力学:内源与外源噪声的数学模型及其应用

发布时间：2018-04-12 07:00

  本文选题：Markov链 + 随机映射　； 参考：《中国科学:数学》2017年12期

【摘要】：复杂系统与过程的数学建模需要用随机动力学(stochastic dynamics)的思想和方法.随机动力学的理论有着两种不同的数学表述:随机过程(stochastic processes)和随机动力系统(random dynamical systems).后者是比前者更为精细的数学模型,它不但给出对应于每一个初值的随机过程,还全面地描述不同初值的多条随机轨道如何同时随时间变化.前者恰恰表述了有内在随机性的个体的运动,而后者则反映了多个相同的确定性个体同时经历同一个随机环境.本文称这两种情形为内源噪声和外源噪声.两者都在化学和生物学中有广泛的应用.近年来兴起的以图G(V,E)为基础的概率布尔网络正是一类以{0,1}~V为状态空间的随机动力系统(RDS).本文介绍有关离散时间离散空间的RDS,同时也给出一个它在统计推断隐Markov模型的收敛速率估算中的应用.
[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.
【作者单位】： Department
【分类号】：O19
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本文编号：1738664