Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

Sau Fa K.; Wang K.G.

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Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

机译：与连续时间随机游动相关的相空间联合概率密度的积分微分方程

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We derive an integro-differential equation for the joint probability density function in phase space associated with the continuous-time random walk, with generic waiting time probability density function and external force. This equation permits us to investigate whole diffusion processes covering initial-, intermediate-, and long-time ranges, which can distinguish the evolution details for systems having the same behavior in the long-time limit with different initial- and intermediate-time behaviors. Moreover, we obtained analytic solutions for probability density functions both in velocity and phase spaces, and interesting dynamic behaviors are discovered.

机译：我们用连续等待时间概率密度函数和外力推导了与连续时间随机行走相关的相空间中联合概率密度函数的积分微分方程。该方程式使我们能够研究涵盖初始，中间和长时间范围的整个扩散过程，从而可以区分具有相同初始行为和中间行为的长时间限制内具有相同行为的系统的演化细节。此外，我们获得了速度和相空间中概率密度函数的解析解，并发现了有趣的动力学行为。

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《Physica, A. Statistical mechanics and its applications》 |2012年第15期|共7页
作者
Sau Fa K.; Wang K.G.;
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正文语种 eng
中图分类物理学;
关键词
Anomalous diffusion; Continuous-time random walk; Probability density function;

机译：异常扩散连续时间随机游动概率密度函数;

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专利

1. Integro-differential equation for joint probability density in phase space associated with continuous-time random walk [J] . Sau Fa K., Wang K.G. Physica, A. Statistical mechanics and its applications . 2012,第15期

机译：与连续时间随机游动相关的相空间联合概率密度的积分微分方程
2. Uncoupled continuous-time random walk: Finite jump length probability density function [J] . Fa K.S. Journal of physics, A. Mathematical and theoretical . 2012,第19期

机译：非耦合连续时间随机游动：有限跳跃长度概率密度函数
3. A fractional diffusion equation for two-point probability distributions of a continuous-time random walk [J] . A. Baule, R. Friedrich EPL . 2007,第1期

机译：连续时间随机游动的两点概率分布的分数阶扩散方程
4. From Continuous-Time Random Walks to Continuous-Time Quantum Walks: Disordered Networks [C] . Oliver Muelken, Alexander Blumen NATO advanced research workshop on new challenges in complex systems: Disaster forecasting, crisis modeling and sustainable development . 2014

机译：从连续时间随机散步到连续时间量子播放：无序网络
5. Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space. [D] . Donnelly, Roderick Kerry. 1988

机译：对分析的一些贡献：涉及Hilbert变换的积分微分方程的广义函数的新空间，以及关于Hilbert空间上测试函数的空间的非核性的注释。
6. Joint coverage probability in a simulation study on Continuous-Time Markov Chain parameter estimation [O] . Julia S. Benoit, Wenyaw Chan, Rachelle S. Doody -1

机译：连续时间马尔可夫链参数估计的仿真研究中的联合覆盖概率
7. A fractional diffusion equation for two-point probability distributions of a continuous-time random walk [O] . A Baule, R Friedrich 2007

机译：连续时间随机行走两点概率分布的分数扩散方程
8. The Phase Probability Density Function of a Random Walk in Two Dimensions [R] . Barber, B. C. 1982

机译：二维随机游动的相位概率密度函数

Integro-differential equation for joint probability density in phase space associated with continuous-time random walk

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