Stochastic modelling with randomized Markov bridges
Stochastic modelling with randomized Markov bridges
复制标题
使用随机马尔可夫桥的随机建模
DOI：
10.1080/17442508.2019.1703988
复制
发表时间：
2019
期刊：
影响因子：
0.9
通讯作者：
Andrea Macrina and Jun Sekine
中科院分区：
文献类型：
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作者：
Masaaki Fukasawa;Hitomi Maeda;and Jun Sekine;関根 順;関根 順;関根 順;関根 順;Andrea Macrina and Jun Sekine
本文研究了由噪声观测值估计隐随机变量X的滤波问题。噪声观测过程由随机马尔可夫桥（RMB）构成，其终值设置为。也就是说，在终端时间T，桥过程的噪声消失，隐藏的随机变量X被揭示出来。我们推导了一般人民币的条件概率过程的动力学的显式过滤公式。结果表明，条件概率由当前时间、当前观测值、初始观测值和Xatt = 0的优先分布ν的函数给出。作为一个例子，人民币，我们明确地构建了偏态随机扩散桥，并展示了如何利用它来扩展知名的商品定价模型，以及如何提出新的随机价格模型的金融工具与温室气体排放。
We consider the filtering problem of estimating a hidden random variableXby noisy observations. The noisy observation process is constructed by a randomized Markov bridge (RMB)of which terminal value is set to. That is, at the terminal timeT, the noise of the bridge process vanishes and the hidden random variableXis revealed. We derive the explicit filtering formula, governing the dynamics of the conditional probability process, for a general RMB. It turns out that the conditional probability is given by a function of current timet, the current observation, the initial observation, and thea prioridistributionνofXatt= 0. As an example for an RMB, we explicitly construct the skew-normal randomized diffusion bridge and show how it can be utilized to extend well-known commodity pricing models and how one may propose novel stochastic price models for financial instruments linked to greenhouse gas emissions.