A law of large numbers for the possibilistic mean value of a variable in a possibility space is presented. An example shows that the convergence in distribution (under a definition involving the possibilistic mean value) of the sample average to a variable with a certain distribution cannot be replaced, in general, by convergence either almost surely or in necessity. Even so, the usual presenta...

Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an extension to upper enveloppe measures.

We introduce the notion of the mean-set (expectation) of a graph(group-) valued random element ξ and prove a generalization of the strong law of large numbers on graphs and groups. Furthermore, we prove an analogue of the classical Chebyshev’s inequality for ξ. We show that our generalized law of large numbers, as a new theoretical tool, provides a framework for practical applications; namely, ...

Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑N n=1 f(n)Xn ∑N n=1 f(n) = EX a.s.

In this paper, we propose a class of nonlinear expectations induced by backward stochastic differential equations and reflected backward stochastic differential equations and prove the law of large numbers under the nonlinear expectation.

Our purpose in this article is to show that if P is any probability measure on N such that P({ν}) > 0 for every ν ∈ N, then the set of all sequences of random variables on the probability measure space (N,P(N),P) which are in L(N,P) and satisfy the law of large numbers is Π3-complete.

Abstract. We construct new examples of cylinder flows, given by skew product extensions of irrational rotations on the circle, that are ergodic and rationally ergodic along a subsequence of iterates. In particular, they exhibit law of large numbers. This is accomplished by explicitly calculating, for a subsequence of iterates, the number of visits to zero, and it is shown that such number has a...

In this paper we present a form of law of large numbers on Pn, the space of n× n symmetric positive-definite (SPD) matrices equipped with Fisher-Rao metric. Specifically, we propose a recursive algorithm for estimating the Karcher expectation of an arbitrary distribution defined on Pn, and we show that the estimates computed by the recursive algorithm asymptotically converge in probability to t...

In the spirit of a classical result for Crump–Mode–Jagers processes, we prove a strong law of large numbers for fragmentation processes. Specifically, for self-similar fragmentation processes, including homogenous processes, we prove the almost sure convergence of an empirical measure associated with the stopping line corresponding to first fragments of size strictly smaller than η for 1 ≥ η > ...

Abstract. This work considers a many-server queueing system in which customers with i.i.d., generally distributed service times enter service in the order of arrival. The dynamics of the system are represented in terms of a process that describes the total number of customers in the system, as well as a measure-valued process that keeps track of the ages of customers in service. Under mild assu...