An Asymptotic Analysis of the Spatially Inhomogeneous Velocity-Jump Process
An Asymptotic Analysis of the Spatially Inhomogeneous Velocity-Jump Process
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空间非均匀速度跳跃过程的渐近分析
DOI：
10.1137/10080676x
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
J. Keener
中科院分区：
文献类型：
--
作者：
J. Newby;J. Keener
我们分析了一维速度跳跃过程，其中粒子以恒定速度移动，该速度由粒子的内部速度状态决定，该速度状态随机波动，等待时间呈指数分布。内部速度状态之间的转换率取决于粒子的位置，导致空间不均匀的随机过程。应用渐近分析获得随机过程的平稳分布。结果相比，经常使用的准稳态扩散近似，它被发现，扩散近似打破了在存在一个转折点，在那里的粒子的平均速度改变符号。我们扩展的分析近似的第一个出口的时间密度的粒子逃脱限制的转折点的影响，我们发现扩散近似也未能准确地描述的长时间的行为的过程。这两个近似的准确性进行了探讨，为一个…
We analyze the one-dimensional velocity-jump process, where a particle moves at a constant velocity determined by the particle’s internal velocity state that randomly fluctuates with exponentially distributed waiting times. The transition rates between the internal velocity states depend on the location of the particle, leading to a spatially inhomogeneous random process. An asymptotic analysis is applied to obtain the stationary distribution of the random process. The result is compared to the often-used quasi–steady-state diffusion approximation, and it is found that the diffusion approximation breaks down in the presence of a turning point, where the average velocity of the particle changes sign. We extend the analysis to approximate the first-exit time density for the particle to escape the confining effect of the turning point, and we find the diffusion approximation also fails to accurately describe the long-time behavior of the process. The accuracy of the two approximations is explored for a simpl...
DOI：
10.1073/pnas.83.11.4044
发表时间：
1986-06-01
影响因子：
11.1
作者：
KOSIK, KS;JOACHIM, CL;SELKOE, DJ
通讯作者：
SELKOE, DJ