Department of Condensed Matter Physics and Institute of Complex Systems (UBICS), University of Barcelona, Catalonia, Spain.
Phys Rev E. 2019 Jan;99(1-1):012121. doi: 10.1103/PhysRevE.99.012121.
We investigate the effects of resetting mechanisms on random processes that follow the telegrapher's equation instead of the usual diffusion equation. We thus study the consequences of a finite speed of signal propagation, the landmark of telegraphic processes. Likewise diffusion processes where signal propagation is instantaneous, we show that in telegraphic processes, where signal propagation is not instantaneous, random resettings also stabilize the random walk around the resetting position and optimize the mean first-arrival time. We also obtain the exact evolution equations for the probability density of the combined process and study the limiting cases.
我们研究了在遵循电报方程而不是通常的扩散方程的随机过程中重置机制的影响。因此，我们研究了信号传播速度有限的后果，这是电报过程的标志。同样，在信号传播瞬时的扩散过程中，我们表明，在信号传播非瞬时的电报过程中，随机重置也会稳定随机游走在重置位置附近，并优化平均首次到达时间。我们还获得了组合过程的概率密度的精确演化方程，并研究了极限情况。
