Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distributio...

This note proposes convergence analysis of iterative learning control (ILC) for discrete-time linear systems with randomly varying iteration lengths. No prior information is required on the probability distribution of randomly varying iteration lengths. The conventional P-type update law is adopted with Arimoto-like gain and/or causal gain. The convergence both in almost sure and mean square se...

Standard least mean square/fourth (LMS/F) is a classical adaptive algorithm that combined the advantages of both least mean square (LMS) and least mean fourth (LMF). The advantage of LMS is fast convergence speed while its shortcoming is suboptimal solution in low signal-to-noise ratio (SNR) environment. On the contrary, the advantage of LMF algorithm is robust in low SNR while its drawback is ...

In this paper we prove rates of uniform strong convergence, convergence rates of the mean square error and the asymptotic normality of the kernel estimator for the transition density of a geometrically ergodic Markov chain. The assumptions on the Markov chain are closely related to absolute regularity. We allow the initial distribution of the Markov chain to be arbitrary.

The mean-reverting square root process is a stochastic differential equation (SDE) that has found considerable use as a model for volatility, interest rate, and other financial quantities. The equation has no general, explicit, solution, although its transition density can be characterized. For valuing path-dependent options under this model, it is typically quicker and simpler to simulate the ...

A standard algorithm for LMS-filter simulation, tested with several convergence criteria is presented in this paper. We analyze the steady-state mean square error (MSE) convergence of the LMS algorithm when random functions are used as reference inputs. In this paper, we make a more precise analysis using the deterministic nature of the reference inputs and their time-variant correlation matrix...

This paper studies the rate of convergence of a family of continuous-time Markov chains (CTMC) to a mean-field model. When the mean-field model is a finite-dimensional dynamical system with a unique equilibrium point, an analysis based on Stein’s method and the perturbation theory shows that under some mild conditions, the stationary distributions of CTMCs converge (in the mean-square sense) to...