Large Deviation Theorem for Empirical Measures of Degenerate Diffusion Processes

A class of multi dimensional degenerate diffusion processes X ε(t) in R r(r≥2) are considered and the asymptotic properties of empirical measures are investigated; here X ε(t) saitisfies the stochastic differential equation dX ε(t)=σ(X ε(t)) d W(t)+B(X ε(t)) d t+ εσ～(X ε(t)) d W(t),ε>0. X ε(t) are small random perturbations of the degenerate diffusion process X(t), which satisfies the stochastic differential equation dX(t)=σ(X(t)) d W(t)+B(X(t)) d t. A large deviation theorem for projection measures ν on R r-n (n<r) of empirical measures μ are proved

WEAK LIMITS OF EMPIRICAL MEASURES FOR A FAMILY OF DIFFUSION PROCESSES

This paper considers diffusion processes {X^(?)(t)} on R^2, which are perturbations of dynamical system {X(t)} (dX(t)=b(X(t))dt) on R^2. By means of weak convergence of probability measures, the authors characterize the limit behavior for empirical measures of {X^(?)(t)} in a neighborhood domain of saddle point of the dynamical system as the perturbations tend to zero.

ON THE MEASURABILITY FOR FUNCTIONAL OF EMPIRICAL PROCESSES

In this paper, we give some results for checking the measurability of functional of empirical processes, their direct applications concern with the measurability of statis-tics constructed by Projection pursuit technique, thus the results obtained provide a basis in theory for projection pursuit study.

RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.

Upper Large Deviations for Mixing Random Sequence

In this article, we prove upper large deviations for the empirical measure generated by stationary mixing random sequence under some suitable assumptions and upper large deviations for the mixing random sequence.

Stochastic Systems Arising from Markov Modulated Empirical Measures

This work is devoted to stochastic systems arising from empirical measures of random sequences(termed primary sequences) that are modulated by another Markov chain. The Markov chain is used to model random discrete events that are not represented in the primary sequences. One novel feature is that in lieu of the usual scaling in empirical measure sequences, the authors consider scaling in both space and time, which leads to new limit results. Under broad conditions, it is shown that a scaled sequence of the empirical measure converges weakly to a number of Brownian bridges modulated by a continuous-time Markov chain. Ramifications and special cases are also considered.

Large deviations for empirical measures of switching diffusion processes with small parameters

We consider the asymptotic property of the diffusion processes with Markovian switching. For a general case, we prove a large deviation principle for empirical measures of switching diffusion processes with small parameters.

Unified Limits and Large Deviation Principles forβ-Laguerre Ensembles in Global Regime

Let(λ_(1),...,λ_(n)) be β-Laguerre ensembles with parametersβ,p,n and μ_(n):=1/n∑^(n)_(i=1)δ_(Xi) with for 1≤i≤n.In this paper,asβvaries and satisfies lim_(n→∞)log n/βn=0,we offer a modified Marchenko-Pastur,law or semicircle law as the weak limits for the sequence μ_(n) when lim_(n→∞)n/p=γ∈(0,1]or lim_(n→∞)n/p=0,respectively.This recovers some well-known results.Moreover,we give a full large deviation principle of μ_(n) with speed βn^(2) and good rate function I_(γ) under the same condition to characterize the speed of the convergence.The minimizer of I_(γ) is a modified Marchenko-Pastur law forγ∈(0,1]and the semicircle law forγ=0.

Reliability Evaluation of IEEE 802.11p-Based Vehicle-to-Vehicle Communication in an Urban Expressway

IEEE 802.11p/DSRC （Dedicated Short Range Communication） is considered to be a promising wireless communication standard for enhancing transportation safety and efficiency. However, IEEE 802.11p-based Vehicle- to-Vehicle （V2V） communication is still unreliable because of the complicating factors of high vehicle speed and complex radio environments. In this paper, we performed a data-based evaluation of V2V communication reliability, using real-world measurements in a typical urban expressway in Beijing. With respect to the characteristics of the urban expressway and our experimental data, we found road slope and traffic density to be the major environmental factors having a significant impact on the V2V communication＇s Line-Of-Sight （LOS） conditions. On the basis of these two factors, we propose a fuzzy classification method for the LOS conditions, and separate the real- time communication environments into different LOS cases. For each LOS case, we quantify the metrics as received signal strength indication, packet delivery rate, and communication latency. The results reveal that the communication reliability in urban expressways is very unstable because of the changing LOS conditions. This study provides a useful reference for the IEEE 802.11 p-based cooperative systems in urban expressways.

LARGE DEVIATIONS FOR STATIONARY Φ-MIXING SEQUENCES IN τ-TOPOLOGY

The results of Bryc on large deviations for empirical measures of stationary Φ-mixing sequences are extended. Bryc states his results in the usual weak topology on the space ofprobability measures. In this paper, under somewhat weaker assumptions than those of Bryc,the author extends Bryc's results by taking the finer topology which is generated by the integralsover bounded measurable functions.