Almost sure exponential stability of hybrid stochastic functional differential equations

This paper is concerned with the almost sure exponential stability of the n -dimensional nonlinear hybrid stochastic functional differential equation (SFDE) dx(t)=f(ψ1(xt,t),r(t),t)dt+g(ψ2(xt,t),r(t),t)dB(t), where xt={x(t+u):−τ≤u≤0} is a C([−τ,0];Rn)C([−τ,0];Rn)-valued process, B(t)B(t) is an m -dimensional Brownian motion while r(t) is a Markov chain. We show that if the corresponding hybrid stochastic differential equation (SDE) dy(t)=f(y(t),r(t),t)dt+g(y(t),r(t),t)dB(t) is almost surely exponentially stable, then there exists a positive number τ⁎ such that the SFDE is also almost surely exponentially stable as long as τ<τ⁎. We also describe a method to determine τ⁎ which can be computed numerically in practice

Research on the Effectiveness of the Confucius Institute (Classroom) Based on Linear Regression Models

China has invested heavily in development of the Confucius Institute (Classroom) for the going-global of Chinese language and culture. And its effectiveness evaluation is an essential reference to the reinvestment on the Confucius Institute (Classroom) development as well as to its budget reallocation. Considering that there were basically no such researches in this field ever before, linear regression models (LRMs) were employed in this paper to research the effectiveness of Confucius Institute and establish fitting function models between inputs and outputs, which could provide a tool to quantitatively evaluate the effectiveness in the future. And in this way, the conclusions could be more objective and bases of resource redistribution more scientific. Based on current data, it is found that the growth of the number of government-sponsored Chinese teachers and volunteers lags behind that of the "rigid Chinese language learners" for more than 2 years; If China invests 1,000 Yuan in the project of "the Salary and Training Fee of Chinese Deans and Teachers (including Volunteers) " , the number of the "rigid Chinese language learners" will rise by 10 to 13; if there is an additional overseas test center in the Confucius Institute (Classroom), the "rigid Chinese language learners" of this semester will rise by more than 5,927; and if there is an additional registered student in the Confucius Institute (Classroom), it will rise by more than 6

A New Paradigm for the Etymology and Trend Study from the Perspective of Culturomics

As an emerging discipline in 2011, culturomics belongs to cultural studies mainly by way of diachronic research and large-scale corpora, so it could be significative for the etymology and trend studies. In this paper, a large-scale diachronic corpus was established based on culturomics, and the condition and quality basic-level category vocabulary (BLCV) is taken as examples for analyses, so as to obtain relevant data and conclusions. It is shown that about 90% of the condition and quality BLCV was originated earlier than Sui, Tang and the Five Dynasties, and the first-level BLCV is earlier than the second-level and the third-level in aspect of origin time. The higher BLCV level, the greater the use rate increase, with more obvious stable development in the diachronic respect. Thus, culturomics, as a new paradigm in linguistic researches, is confirmed to be feasible, distinctive and irreplaceable in an era of big data

Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments

In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the -methods are obtained. Some examples are illustrated

Numerical Solutions of Stochastic Differential Delay Equations with Poisson Random Measure under the Generalized Khasminskii-Type Conditions

The Euler method is introduced for stochastic differential delay equations (SDDEs) with Poisson random measure under the generalized Khasminskii-type conditions which cover more classes of such equations than before. The main aims of this paper are to prove the existence of global solutions to such equations and then to investigate the convergence of the Euler method in probability under the generalized Khasminskii-type conditions. Numerical example is given to indicate our results

Numerical Solutions of Stochastic Differential Equations Driven by Poisson Random Measure with Non-Lipschitz Coefficients

The numerical methods in the current known literature require the stochastic differential equations SDEs driven by Poisson random measure satisfying the global Lipschitz condition and the linear growth condition. In this paper, Euler&apos;s method is introduced for SDEs driven by Poisson random measure with non-Lipschitz coefficients which cover more classes of such equations than before. The main aim is to investigate the convergence of the Euler method in probability to such equations with non-Lipschitz coefficients. Numerical example is given to demonstrate our results