To assess whether a given time series can be modeled by a stochastic process possessing long range correlation, one usually applies one of two types of analysis methods: the spectral method and the random walk analysis. The first objective of this work is to show that each one of these methods used alone can be susceptible to producing false results. We thus advocate an integrated approach whic...

In this article a continuous-time stochastic model (the Ornstein-Uhlenbeck process) is presented to model the perpetually altering states of the core affect, which is a 2-dimensional concept underlying all our affective experiences. The process model that we propose can account for the temporal changes in core affect on the latent level. The key parameters of the model are the average position ...

The problem of determining directional coupling between neuronal oscillators from their time series is addressed. We compare performance of the two well-established approaches: partial directed coherence and phase dynamics modeling. They represent linear and nonlinear time series analysis techniques, respectively. In numerical experiments, we found each of them to be applicable and superior und...

In this paper we develop a dynamical theory of coevolution in ecological communities. The derivation explicitly accounts for the stochastic components of evolutionary change and is based on ecological processes at the level of the individual. We show that the coevolutionary dynamic can be envisaged as a directed random walk in the community's trait space. A quantitative description of this stoc...

We classify the rare events of structured, memoryful stochastic processes and use this to analyze sequential and parallel generators for these events. Given a stochastic process, we introduce a method to construct a process whose typical realizations are a given process' rare events. This leads to an expression for the minimum memory required to generate rare events. We then show that the recen...

The iterated Prisoner's Dilemma (IPD) is usually analysed by evaluating arithmetic mean pay-offs in an ESS analysis. We consider several points that the standard argument does not address. Finite population size and finite numbers of matches in the IPD game lead us to consider both pay-off variance and the sampling process in the evolutionary game. We provide a general form for the pay-off vari...

In this paper, the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time-varying delays. The fuzzy system is based on the Takagi-Sugeno (T-S) model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning. To reflect more realistic dynamical behaviors of the system, both the parameter unc...

The aim of this paper is to provide a more realistic description of priority-discipline queueing models by using Fuzzy Set Theory. It develops and optimizes two fuzzy queueing models with priority-discipline, a model with nonpreemptive priorities system and a model with preemptive priorities system, denoted by M̃i /M̃i /1 and M̃i /Fi /1. The first symbol is for a queueing system where arrivals and...

In this paper we study how to make joint extensions of stochastic orderings and interval orderings so as to extend methods for comparing random variables, from the point of view of their respective location or magnitude, to fuzzy random variables. The main idea is that the way fuzzy random variables are interpreted affects the choice of the comparison methods. We distinguish three views of fuzz...