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...

Constructing large Generalized Stochastic Petri Nets (GSPN) by hierarchical composition of smaller components is a promising way to cope with the complexity of the design process for models of real hardware and software systems. The composition of nets is inspired by process algebraic operators. A solid theoretical framework of such operators relies on equivalences that are substitutive with re...

1. Discrete-Event Stochastic Systems Recall our previous definition of a discrete-event stochastic system: the system makes stochastic state transitions only at an increasing sequence of random times. If X(t) is the state of the system at time t, then a typical sample path of the underlying stochastic process of the simulation, i.e. (X(t): t ≥ 0), looks like this (for a finite or countably infi...

The mean completion time of a stochastic process may be rendered finite and minimised by a judiciously chosen restart protocol, which may either be stochastic or deterministic. Here we study analytically an arbitrary stochastic search subject to an arbitrary restart protocol, each characterised by a distribution of waiting times. By a direct enumeration of paths we construct the joint distribut...

We provide a mapping which translates a model in a coloured stochastic Petri net notation (PEPA nets) into a term of a foundational stochastic process algebra (Stochastic CCS). Our mapping is a compositional static method which translates from one high-level model to another without needing to evaluate the state space of the given PEPA net. The result of the translation is a well-formed input f...