Random motion with gamma-distributed alternating velocities in biological modeling

Kinetic hierarchy and propagation of chaos in biological swarm models

We consider two models of biological swarm behavior. In these models, pairs of particles interact to adjust their velocities one to each other. In the first process, called 'BDG', they join their average velocity up to some noise. In the second process, called 'CL', one of the two particles tries to join the other one's velocity. This paper establishes the master equations and BBGKY hierarchies of these two processes. It investigates the infinite particle limit of the hierarchies at large time-scale. It shows that the resulting kinetic hierarchy for the CL process does not satisfy propagation …

Telegraph random evolutions on a circle

We consider the random evolution described by the motion of a particle moving on a circle alternating the angular velocities $ \pm c $ and changing rotation at Poisson random times, resulting in a telegraph process over the circle. We study the analytic properties of the semigroup it generates as well as its probability distribution. The asymptotic behavior of the wrapped process is also studied in terms of circular Brownian motion. Besides, it is possible to derive a stochastic model for harmonic oscillators with random changes in direction and we give a diffusive approximation of this proces…

动态Erdős-Rényi随机图在状态切换下的推断

Inference for dynamic Erdős-Rényi random graphs under regime switching

本文针对状态切换下两个并行动态Erdős-Rényi随机图，利用聚合观测数据，通过矩估计方法估计边开启/关闭时间分布及模式持续时间，并经实验验证有效性。