摘要翻译:
在随机游动中,格林函数的路径表示是路径概率密度函数长度上的无限和。本文在Laplace空间中导出并求解了任意非齐次半马尔可夫随机游动在一维L态链中的n阶路径PDF的递推关系。该递归关系将n阶路径PDF与L/2(对于奇数L)短路径PDFs相关联,并具有n个服从通用公式的独立系数。递归关系的z变换直接给出了路径PDF的母函数,由此得到了随机游动的格林函数,并导出了任意路径PDF的显式表达式。这些表达式给出了一维任意非齐次半马尔可夫随机游动的最详细的描述。
---
英文标题:
《Path probability density functions for semi-Markovian random walks》
---
作者:
O. Flomenbom and R. J. Silbey
---
最新提交年份:
2007
---
分类信息:
一级分类:Physics 物理学
二级分类:Mathematical Physics 数学物理
分类描述:Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
这一类别的文章集中在说明数学在物理问题中的应用的研究领域,为这类应用开发数学方法,或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣;主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类:Mathematics 数学
二级分类:Mathematical Physics 数学物理
分类描述:math.MP is an alias for math-ph. Articles in this category focus on areas of research that illustrate the application of mathematics to problems in physics, develop mathematical methods for such applications, or provide mathematically rigorous formulations of existing physical theories. Submissions to math-ph should be of interest to both physically oriented mathematicians and mathematically oriented physicists; submissions which are primarily of interest to theoretical physicists or to mathematicians should probably be directed to the respective physics/math categories
math.mp是math-ph的别名。这一类别的文章集中在说明数学在物理问题中的应用的研究领域,为这类应用开发数学方法,或提供现有物理理论的数学严格公式。提交的数学-PH应该对物理方向的数学家和数学方向的物理学家都感兴趣;主要对理论物理学家或数学家感兴趣的投稿可能应该指向各自的物理/数学类别
--
一级分类:Physics 物理学
二级分类:Biological Physics 生物物理学
分类描述:Molecular biophysics, cellular biophysics, neurological biophysics, membrane biophysics, single-molecule biophysics, ecological biophysics, quantum phenomena in biological systems (quantum biophysics), theoretical biophysics, molecular dynamics/modeling and simulation, game theory, biomechanics, bioinformatics, microorganisms, virology, evolution, biophysical methods.
分子生物物理、细胞生物物理、神经生物物理、膜生物物理、单分子生物物理、生态生物物理、生物系统中的量子现象(量子生物物理)、理论生物物理、分子动力学/建模与模拟、博弈论、生物力学、生物信息学、微生物、病毒学、进化论、生物物理方法。
--
一级分类:Quantitative Biology 数量生物学
二级分类:Other Quantitative Biology 其他定量生物学
分类描述:Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
--
---
英文摘要:
In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF for any arbitrarily inhomogeneous semi-Markovian random walk in a one-dimensional (1D) chain of L states. The recursion relation relates the n order path PDF to L/2 (round towards zero for an odd L) shorter path PDFs, and has n independent coefficients that obey a universal formula. The z transform of the recursion relation straightforwardly gives the generating function for path PDFs, from which we obtain the Green's function of the random walk, and derive an explicit expression for any path PDF of the random walk. These expressions give the most detailed description of arbitrarily inhomogeneous semi-Markovian random walks in 1D.
---
PDF链接:
https://arxiv.org/pdf/0706.3211