英文标题：
《Probability measure-valued polynomial diffusions》
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作者：
Christa Cuchiero, Martin Larsson, Sara Svaluto-Ferro
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最新提交年份：
2018
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英文摘要：
We introduce a class of probability measure-valued diffusions, coined polynomial, of which the well-known Fleming--Viot process is a particular example. The defining property of finite dimensional polynomial processes considered by Cuchiero et al. (2012) and Filipovic and Larsson (2016) is transferred to this infinite dimensional setting. This leads to a representation of conditional marginal moments via a finite dimensional linear PDE, whose spatial dimension corresponds to the degree of the moment. As a result, the tractability of finite dimensional polynomial processes are preserved in this setting. We also obtain a representation of the corresponding extended generators, and prove well-posedness of the associated martingale problems. In particular, uniqueness is obtained from the duality relationship with the PDEs mentioned above.
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中文摘要：
我们引入了一类概率测度值扩散，即多项式，其中著名的Fleming-Viot过程就是一个特例。Cuchiero et al.（2012）和Filipovic and Larsson（2016）所考虑的有限维多项式过程的定义性质被转移到这个无限维环境中。这导致通过有限维线性偏微分方程表示条件边际矩，其空间维度对应于矩的阶数。因此，有限维多项式过程的可处理性在此设置中得以保持。我们还得到了相应扩展生成元的一个表示，并证明了相关鞅问题的适定性。特别地，唯一性是从与上述偏微分方程的对偶关系中获得的。
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分类信息：

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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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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