We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [8]. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n−1/2). This is achieved by a very simple co...

The motivation of this work is the study of the error term et (x,ω) in the averaging method for differential equations perturbed by a dynamical system. Results of convergence in distribution for ( e t (x,·) √ ε )ε>0 have been established in Khas’minskii [Theory Probab. Appl. 11 (1966) 211–228], Kifer [Ergodic Theory Dynamical Systems 15 (1995) 1143– 1172] and Pène [ESAIM Probab. Statist. 6 (200...

A sequence (sn) of integers is good for the mean ergodic theorem if for each invertible measure preserving system (X, B, µ, T) and any bounded measurable function f , the averages 1 N P N n=1 f (T sn x) converge in the L 2 (µ) norm. We construct a sequence (sn) that is good for the mean ergodic theorem, but the sequence (s 2 n) is not. Furthermore, we show that for any set of bad exponents B, t...

We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal [BR85]. In order to do this, • We study and compare three notions of convergence of types in a stable theory: logic convergence, i.e., formula by formula, metric convergence (both already well studied) and convergence of canonical bases. In particular, we characterise א0...

Title of dissertation: INTERNATIONAL CORPORATE GOVERNANCE: A STUDY OF COMPLEMENTARITIES AND CONVERGENCE Meghana Ayyagari, Doctor of Philosophy, 2004 Dissertation directed by: Professor Vojislav Maksimovic Department of Finance This thesis contributes to contemporary research in international corporate governance by investigating two related questions: (1) Is there a convergence in corporate gov...

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

Experiments show different plays among identical players and change of reaction rules (how plays are adjusted after an observation) over time. These phenomena are not easily incorporated in adaptive learning models. We model a sophisticated learning model, where players hold “theories” which map information to beliefs using the knowledge of the game and rationality. For example, a player can th...

In this paper, we show that the main results of the local convergence theory for least-change secant update methods of Dennis and Walker (SIAM J. Numer. Anal. 18 (1981), 949-987) can be proved using the theory introduced recently by Martinez (Math. Comp. 55 (1990), 143-167). In addition, we exhibit two generalizations of well-known methods whose local convergence can be easily proved using Mart...

Recent convergence analyses of evolutionary pattern search algorithms (EPSAs) have shown that these methods have a weak stationary point convergence theory for a broad class of unconstrained and linearly constrained problems. This paper describes how the convergence theory for EPSAs can be adapted to allow each individual in a population to have its own mutation step length (similar to the desi...

We propose a general formalism of iterated random functions with semigroup property, under which exact and approximate Bayesian posterior updates can be viewed as specific instances. A convergence theory for iterated random functions is presented. As an application of the general theory we analyze convergence behaviors of exact and approximate message-passing algorithms that arise in a sequenti...