Exponential change of measure for general piecewise deterministic Markov processes
Exponential change of measure for general piecewise deterministic Markov processes
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DOI：
10.1007/s11425-017-9345-5
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Zhaoyang Liu;Yuying Liu;Guoxin Liu
中科院分区：
文献类型：
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作者：
Zhaoyang Liu;Yuying Liu;Guoxin Liu
我们考虑一个具有测量值生成器a的一般分段确定性马尔可夫过程（PDMP） X= X t t小于0，其中间隔发生时间的条件分布函数不一定是绝对连续的。与X相关的指数鞅的一般形式是M＿t^ f= f (X＿t) f (X＿0) \left S \exp ((0, t dL (Af) ＿g f (x＿g -)) \right ^-1。M tf= f (X t) f (X 0) S exp(∫(0,t) d L (A f) gf (X g−))−1。通过考虑该指数鞅是一个似然比过程，我们定义了一个新的概率测度，并证明了在新的概率测度下，过程X仍然是一个一般的PDMP。此外，我们还找到了新的测量值生成器及其定义域。为了说明我们的结果，我们研究了连续时间复合二项式模型。
We consider a general piecewise deterministic Markov process (PDMP) X= X t t⩾ 0 with a measure-valued generator A, for which the conditional distribution function of the inter-occurrence time is not necessarily absolutely continuous. A general form of the exponential martingales that are associated with X is given by M_t^ f= f (X_t) f (X_0)\left S\exp ((0, t dL (Af) _g f (X_ g-))\right^-1. M tf= f (X t) f (X 0) S exp (∫(0, t d L (A f) gf (X g−))− 1. By considering this exponential martingale to be a likelihood-ratio process, we define a new probability measure and show that the process X is still a general PDMP under the new probability measure. We additionally find the new measure-valued generator and its domain. To illustrate our results, we investigate the continuous-time compound binomial model.