论文标题
在固定随机力的作用下，无限的谐波振荡器链
Infinite Chain of Harmonic Oscillators Under the Action of the Stationary Stochastic Force
论文作者
论文摘要
我们认为，在实际线路上具有可数的谐波振荡器系统，具有二次相互作用的潜力，以及仅作用于一个固定粒子上的有限支撑和局部外力（固定随机过程）。在$ L_2（\ Mathbb {Z}）$中的正确定潜力和初始条件的情况下，空间可以发现粒子与平衡点的偏差的依从性。确切地说，每个粒子的偏差可以表示为某些固定过程的总和（这也是该函数的分布时间限制过程），而将其收敛到零为$ t \ rightarrow+\ iffty $具有概率一个。也发现了整个系统的平均能量的时间限制。
We consider countable system of harmonic oscillators on the real line with quadratic interaction potential with finite support and local external force (stationary stochastic process) acting only on one fixed particle. In the case of positive definite potential and initial conditions lying in $l_2(\mathbb{Z})$-space the perpesentation of the deviations of the particles from their equilibrium points are found. Precisely, deviation of each particle could be represented as the sum of some stationary process (it is also time limiting process in distribution for that function) and the process which converges to zero as $t\rightarrow+\infty$ with probability one. The time limit for the mean energy of the whole system is found as well.
