英文标题：
《Stationarity of Bivariate Dynamic Contagion Processes》
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作者：
Angelos Dassios, Xin Dong
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最新提交年份：
2014
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英文摘要：
The Bivariate Dynamic Contagion Processes (BDCP) are a broad class of bivariate point processes characterized by the intensities as a general class of piecewise deterministic Markov processes. The BDCP describes a rich dynamic structure where the system is under the influence of both external and internal factors modelled by a shot-noise Cox process and a generalized Hawkes process respectively. In this paper we mainly address the stationarity issue for the BDCP, which is important in applications. We investigate the stationary distribution by applying the the Markov theory on the branching system approximation representation of the BDCP. We find the condition under which there exists a unique stationary distribution of the BDCP intensity and the resulting BDCP has stationary increments. Moments of the stationary intensity are provided by using the Markov property.
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中文摘要：
二元动态传染过程（BDCP）是一类广泛的二元点过程，其特征是强度是一类一般的分段确定马尔可夫过程。BDCP描述了一个丰富的动态结构，其中系统分别受到散粒噪声Cox过程和广义Hawkes过程建模的外部和内部因素的影响。在本文中，我们主要讨论BDCP的平稳性问题，这在应用中很重要。我们将马尔可夫理论应用于BDCP的分支系统近似表示来研究平稳分布。我们找到了BDCP强度存在唯一平稳分布且由此产生的BDCP具有平稳增量的条件。利用马尔可夫性质给出了稳态强度的矩。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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