Under some simple conditions, the convergence of a generalized chaotic system about its all variables is derived by only considering the convergence of its partial variables. Furthermore, based on some inequality techniques and employing the Lyapunov method, some novel sufficient criteria are...

A hidden Markov model (HMM) is said to have path-mergeable states if for any two states i,j there exist a word w and state k such that it is possible to transition from both i and j to k while emitting w. We show that for a finite HMM with path-mergeable states the block estimates of the entropy...

A new kind of recurrent neural network is presented for solving the Lyapunov equation with time-varying coefficient matrices. Different from other neural-computation approaches, the neural network is developed by following Zhang et al.'s design method, which is capable of solving the...

We prove that strong ergodicity of a Markov process is linked with a spectral radius of a certain “associated” semigroup operator, although, not a “natural” one. We also give sufficient conditions for weak ergodicity and provide explicit estimates of the convergence rate. To establish...

This paper presents a Nash equilibrium model where the underlying objective functions involve uncertainty and nonsmoothness. The well-known sample average approximation method is applied to solve the problem and the first order equilibrium conditions are characterized in terms of Clarke...

In this paper we apply the well known sample average approximation (SAA) method to solve a class of stochastic variational inequality problems (SVIPs). We investigate the existence and convergence of a solution to the sample average approximated SVIP. Under some moderate conditions, we show that...