Linear Noise Approximation for a Class of Piecewise Deterministic Markov Processes
Linear Noise Approximation for a Class of Piecewise Deterministic Markov Processes
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一类分段确定性马尔可夫过程的线性噪声逼近
DOI：
10.23919/acc.2018.8431767
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Abhyudai Singh
中科院分区：
文献类型：
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作者：
Saurabh Modi;Mohammad Soltani;Abhyudai Singh
分段确定性马尔可夫过程（Pesthetic Markov Process，简称Pesthetic）是一类将离散随机事件与连续确定性动力学相结合的数学模型。由于物理系统中存在的非线性，通常无法获得Pdq的精确解，通过Pdq进行建模。毫不奇怪，研究人员使用各种近似方法来获得PdR统计矩的分析结果。在本文中，我们的目标是扩展的线性噪声近似（LNA）的方法，以PSNR。LNA方法是通过主方程概率分布解的小噪声近似得到的，广泛应用于离散状态连续时间模型。我们证明，LNA是只直接适用于一个小的子类的PSTK，我们表明，对于这个子类，LNA是相当于直接计算的时刻，通过线性化系统的非线性。最后，对于直接应用低噪声放大器通过欧米茄展开无法给出有意义的结果的系统，我们提供了一种新的方法近似的时刻。
Piecewise deterministic Markov processes (PDMP) are a class of mathematical models that integrates discrete stochastic events with continuous deterministic dynamics. The exact solution of PDMP is usually not available due to nonlinearities present in the physical systems at which are modeled via PDMP. Not surprisingly researchers use a variety of approximations to obtain analytical results of statistical moments of PDMP. In this paper we aim to extend the Linear Noise Approximation (LNA) method to PDMP. The LNA method is obtained by small noise approximation of the probability distribution solution of the master equation, and is widely used in discrete-state continuous-time models. We prove that LNA is only directly applicable to a small sub-class of PDMP, and we show that for this sub-class, LNA is equivalent to calculating moments directly by linearizing nonlinearities of the system. Finally for the systems where direct application of LNA via omega expansion fails to give meaningful results, we provide a novel method for approximating moments.
DOI：
10.1109/cdc.2017.8263922
发表时间：
2017-03
期刊：
2017 IEEE 56th Annual Conference on Decision and Control (CDC)
影响因子：
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作者：
K. Ghusinga;Mohammad Soltani;Andrew G. Lamperski;S. Dhople;Abhyudai Singh
通讯作者：
K. Ghusinga;Mohammad Soltani;Andrew G. Lamperski;S. Dhople;Abhyudai Singh