具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛(英文)

Weak Convergence of Stochastic Recurrent Neural Networks with Markovian Switching and Time-varying Delay

本文研究了具有变时滞和马尔可夫切换的随机递归神经网络的弱收敛,通过运用Lyapunov函数、随机分析技巧和推广了的Halanay不等式,得到了上述模型为弱收敛的充分性条件,并且我们揭示了对上述递归神经网络模型所确定的segment过程的转移概率的极限分布是此模型的解过程的唯一的遍历不变概率测度.此外,我们还给出了例子和数值模拟来说明我们结论的正确性.

This paper is concerned with the weak convergence of stochastic recurrent neural networks with Markovian switching and time- varying delay. By using Lyapunov function,stochastic analysis technique and generalized Halanay inequality,some sufficient conditions on weak convergence are given. For such recurrent neural networks,it reveals that the limit distribution of transition probability for segment process associated with solution process is indeed a unique ergodic invariant probability measure. Moreover,an example and numerical simulation are provided to demonstrate the effectiveness and applicability of the theoretical results.