Theorem 1. Let {Xn}n=1 ⊂ L∞(T ) be a sequence of stochastic processes on T . The followings are equivalent. (1) Xn converge in distribution to a tight stochastic process X ∈ L∞(T ); (2) both of the followings: (a) Finite Dimensional Convergence (FIDI): for every k ∈ N and t1, · · · , tk ∈ T , (Xn(t1), · · · , Xn(tk)) converge in distribution as n→∞; (b) the sequence {Xn} is asymptotically stoch...

The test misgrading is treated in this paper as a stochastic process. Three characteristic values, the expected number of misgradings, the expected inter-occurrence time of misgradings, and the expected waiting time for the nth misgrading, are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Regular tests for classroom teaching and the Test of Written English (TW...

Although market observations show that correlation between stocks, interest rates, e. g., is not deterministic, correlation is usually modelled as a fixed number. This article provides a new approach of modelling correlation as a stochastic process which has applications in many fields. We will show an example from financial markets where the stochasticity of correlation is a fundamental source...

[2] Probabilistic network representations of continuous-time stochastic processes for applications in planning and control. [5] Hierarchical planning involving deadlines, travel time and resources.

In this contribution we deal with the deterministic dominance of the proba bility moments of stochastic processes More precisely given a positive stochastic process we propose to dominate its probability moment sequence by the trajectory of appropriate lower and upper dominating deterministic processes The analysis of the behavior of the original stochastic process is then transferred to the st...

Since the T-S fuzzy system can approximate any nonlinear system with arbitrary accuracy, it is also expected to be a suitable approach to observe the states of a stochastic nonlinear system. Up to date, a few state estimators for stochastic T-S fuzzy systems have been proposed and applied to various fields without rigorous proof. In this paper, we first derive a sufficient condition based on th...

This work presents the development of a methodology based on Monte Carlo Simulation, Fuzzy Numbers and in the Real Options Theory to determine the real options value under technical and market uncertainties. The objective of the proposed methodology is to substantially reduce the computational time involved, facilitating the decision taking process. The methodology involves: fuzzy numbers, to r...

Two major approaches to deal with randomness or impression involved in mathematical programming problems have been developed. The one is called stochastic programming, and the other is called fuzzy programming. In this paper, we focus on multiobjective integer programming problems involving random variable coefficients in constraints. Using the concept of simple recourse, such multiobjective st...