英文标题：
《Path Diffusion, Part I》
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作者：
Johan GB Beumee, Chris Cormack, Peyman Khorsand, Manish Patel
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最新提交年份：
2014
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英文摘要：
This paper investigates the position (state) distribution of the single step binomial (multi-nomial) process on a discrete state / time grid under the assumption that the velocity process rather than the state process is Markovian. In this model the particle follows a simple multi-step process in velocity space which also preserves the proper state equation of motion. Many numerical numerical examples of this process are provided. For a smaller grid the probability construction converges into a correlated set of probabilities of hyperbolic functions for each velocity at each state point. It is shown that the two dimensional process can be transformed into a Telegraph equation and via transformation into a Klein-Gordon equation if the transition rates are constant. In the last Section there is an example of multi-dimensional hyperbolic partial differential equation whose numerical average satisfies Newton\'s equation. There is also a momentum measure provided both for the two-dimensional case as for the multi-dimensional rate matrix.
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中文摘要：
在速度过程而非状态过程是马尔可夫过程的假设下，研究了离散状态/时间网格上单步二项（多项式）过程的位置（状态）分布。在这个模型中，粒子在速度空间中遵循一个简单的多步过程，这也保留了适当的运动状态方程。文中给出了这一过程的许多数值例子。对于较小的网格，概率结构收敛为每个状态点的每个速度的双曲函数的相关概率集。结果表明，当跃迁速率为常数时，二维过程可以转化为电报方程，也可以转化为Klein-Gordon方程。在最后一节中，有一个多维双曲偏微分方程的例子，其数值平均值满足牛顿方程。对于二维情况和多维速率矩阵，也提供了动量度量。
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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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