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...

We develop a unifying approach for approximating a “limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or “almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

We present in this paper several asymptotic properties of constrained Markov Decision Processes (MDPs) with a countable state space. We treat both the discounted and the expected average cost, with unbounded cost. We are interested in (1) the convergence of nite horizon MDPs to the innnite horizon MDP, (2) convergence of MDPs with a truncated state space to the problem with innnite state space,...

In this paper we derive convergence rates for Q-learning. We show an interesting relationship between the convergence rate and the learning rate used in Q-learning. For a polynomial learning rate, one which is 1/t at time t where ω ∈ (1/2, 1), we show that the convergence rate is polynomial in 1/(1− γ), where γ is the discount factor. In contrast we show that for a linear learning rate, one whi...

We develop a unifying approach for approximating a \limit" zero-sum game by a sequence of approximating games. We discuss both the convergence of the values and the convergence of optimal (or \almost" optimal) strategies. Moreover, based on optimal policies for the limit game, we construct policies which are almost optimal for the approximating games. We then apply the general framework to stat...

Let E be the union of two real intervals not containing zero. Then Ln(E) denotes the supremum norm of that polynomial Pn of degree less than or equal to n, which is minimal with respect to the supremum norm provided that Pn(0) = 1. It is well known that the limit κ(E) := limn→∞ n √ Ln(E) exists, where κ(E) is called the asymptotic convergence factor, since it plays a crucial role for certain it...

This paper applies the Phillips and Sul (2007) method to test for convergence in stock returns to an extensive dataset including monthly stock price indices for five EU countries (Germany, France, the Netherlands, Ireland and the UK) as well as the US between 1973 and 2008. We carry out the analysis on both sectors and individual industries within sectors. As a first step, we use the Stock and ...