RAZUMIKHIN-TYPE THEOREM FOR NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

This paper establishes the Razumikhin-type theorem on stability for neutral stochastic functional differential equations with unbounded delay. To overcome difficulties from unbounded delay, we develop several different techniques to investigate stability. To show our idea clearly, we examine neutral stochastic delay differential equations with unbounded delay and linear neutral stochastic Volterra unbounded-delay-integro-differential equations.

THE EXISTENCE AND UNIQUENESS OF SOLUTION FOR A CLASS OF STOCHASTIC FUNCTIONAL EQUAFIONS ON S.P.SPACE

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X =φ(X), where φ: B → B and B is a Banach space consisted of all left-continuous, (■_t)-adapted processes. Also, the main result is applied to some S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the ekistence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

RAZUMIKHIN-TYPE THEOREMS OF NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

The stability of stochastic functional differential equation with Markovian switching was studied by several authors,but there was almost no work on the stability of the neutral stochastic functional differential equations with Markovian switching.The aim of this article is to close this gap.The authors establish Razumikhin-type theorem of the neutral stochastic functional differential equations with Markovian switching,and those without Markovian switching.

Razumikhin-Type Theorems on General Decay Stability of Impulsive Stochastic Functional Differential Systems with Markovian Switching

In this paper, the Razumikhin approach is applied to the study of both p-th moment and almost sure stability on a general decay for a class of impulsive stochastic functional differential systems with Markovian switching. Based on the Lyapunov-Razumikhin methods, some sufficient conditions are derived to check the stability of impulsive stochastic functional differential systems with Markovian switching. One numerical example is provided to demonstrate the effectiveness of the results.

Asymptotic and stable properties of general stochastic functional differential equations

The asymptotic and stable properties of general stochastic functional differential equations are investigated by the multiple Lyapunov function method, which admits non-negative up-per bounds for the stochastic derivatives of the Lyapunov functions, a theorem for asymptotic properties of the LaSal e-type described by limit sets of the solutions of the equations is obtained. Based on the asymptotic properties to the limit set, a theorem of asymptotic stability of the stochastic functional differential equations is also established, which enables us to construct the Lyapunov functions more easily in application. Particularly, the wel-known classical theorem on stochastic stability is a special case of our result, the operator LV is not required to be negative which is more general to fulfil and the stochastic perturbation plays an important role in it. These show clearly the improvement of the traditional method to find the Lyapunov functions. A numerical simulation example is given to il ustrate the usage of the method.

ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained, The results show that the wellknown classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.

Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.

Extended Jacobi Elliptic Function Rational Expansion Method and Its Application to （2＋1）-Dimensional Stochastic Dispersive Long Wave System

In this work, by means of a generalized method and symbolic computation, we extend the Jacobi elliptic function rational expansion method to uniformly construct a series of stochastic wave solutions for stochastic evolution equations. To illustrate the effectiveness of our method, we take the （2＋ 1）-dimensional stochastic dispersive long wave system as an example. We not only have obtained some known solutions, but also have constructed some new rational formal stochastic Jacobi elliptic function solutions.

Linear matrix inequality approach for robust stability analysis for stochastic neural networks with time-varying delay

This paper studies the problem of linear matrix inequality （LMI） approach to robust stability analysis for stochastic neural networks with a time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration. Based on the new Lyapunov-Krasovskii functional, some inequality techniques and stochastic stability theory, new delay-dependent stability criteria are obtained in terms of LMIs. The proposed results prove the less conservatism, which are realized by choosing new Lyapunov matrices in the decomposed integral intervals. Finally, numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed LMI method.

Stability of Neutral Stochastic Differential Equations with Multiple Variable Delays

This paper discusses the pth moment stability of neutral stochastic differential equations with multiple variable delays. The equation has a much more general form than the neutral stochastic differential equations with delay. A new kind of φ-function is introduced to address the stability, which is more general than the exponential stability and polynomial stability. Using a specific Lyapunov function, a stability criteria for the neutral stochastic differential equations with multiple variable delays is established, by which it is relatively easy to verify the stability of such equations. Finally, the proposed theories are illustrated by two examples.

RAZUMIKHIN-TYPE THEOREMS FOR ASYMPTOTIC STABILITY OF IMPULSIVE STOCHASTIC FUNCTIONAL DIFFERENTIAL SYSTEMS

In this paper, we investigate the pth moment uniformly asymptotic stability of impulsive stochastic ftmctional differential systems by extending some Razumikhin-type theorems. Based on the Lyapunov functions and Razumikhin techniques, some criteria are established and their applications to impulsive stochastic delay systems are proposed. An illustrative example shows the effectiveness of our results.

The Existence and Uniqueness of the Solution for Neutral Stochastic Functional Differential Equations with Infinite Delay

The main aim of this paper is to establish the existence-and-uniqueness theorem for neutral stochastic functional differential equations with infinite delay at phase space BC（（-∞, 0]; R^n） An example is given for illustration.

Further results on existence-uniqueness for stochastic functional differential equations

The aim of this paper is to develop some basic theories of stochastic functional differential equations (SFDEs) under the local Lipschitz condition in continuous functions space C. Firstly, we establish a global existence-uniqueness lemma for the SFDEs under the global Lipschitz condition in C without the linear growth condition. Then, under the local Lipschitz condition in C, we show that the non-continuable solution of SFDEs still exists if the drift coefficient and diffusion coefficient are square-integrable with respect to t when the state variable equals zero. And the solution of the considered equation must either explode at the end of the maximum existing interval or exist globally. Furthermore, some more general sufficient conditions for the global existence-uniqueness are obtained. Our conditions obtained in this paper are much weaker than some existing results. For example, we need neither the linear growth condition nor the continuous condition on the time t. Two examples are provided to show the effectiveness of the theoretical results.

Mechanization and efficiency in rice production in China

Agricultural mechanization and custom machine services have developed rapidly in China,which can influence rice production efficiency in the future.We calculate technical efficiency,allocative efficiency,and scale efficiency using data collected in 2015 from a face-to-face interview survey of 450 households that cultivated 3096 plots located in the five major rice-producing provinces of China.We use a one-step stochastic frontier model to calculate technical efficiency and regress the efficiency scores on socio-demographic and physical land characteristics to find the influencing variables.Variables influencing technical efficiency are compared at three different phases of rice cultivation.We also calculate technical efficiency by using the Heckman Selection Model,which addresses technological heterogeneity and self-selection bias.Results indicate that:(1)the average value of technical efficiency using a one-step stochastic frontier model was found to be 0.74.When self-selection bias is accounted for using the Heckman Selection Model,the average value of the technical efficiency increases to 0.80;(2)mechanization at the chemical application phase has a positive effect on technical efficiency,but mechanization does not affect efficiency at the plowing and harvesting phases;(3)machines are overused relative to both land and labor,and high machine input use on the small size of landholding has resulted in allocative inefficiency;(4)rice farmers are overwhelmingly operating at a sub-optimal scale.Future policies should focus on encouraging farmland transfer in rural areas to achieve scale efficiency and allocative efficiency while promoting mechanization at the chemical application phase of rice cultivation to improve technical efficiency.

Agricultural Policy, Climate Factors and Grain Output: Evidence From Household Survey Data in Rural China

This paper estimates a stochastic frontier function using a panel data set that includes 4 961 farmer households for the period of 2005-2009 to decompose the growth of grain production and the total factor productivity （TFP） growth at the farmer level. The empirical results show that the major contributor to the grain output growth for farmers is input growth and that its average contribution accounts for 60.92% of farmer’s grain production growth in the period of 2006-2009, whereas the average contributions sourced from TFP growth and residuals are only 17.30 and 21.78%, respectively. The growth of intermediate inputs is a top contributor with an average contribution of 44.46%, followed by the planted area （18.16%）, investment in fixed assets （1.05%）, and labor input （-2.75%）, indicating that the contribution from the farmer’s input growth is mainly due to the growth of intermediate inputs and that the decline in labor inputs has become an obstacle for farmers in seeking grain output growth. Among the elements consisting of TFP growth, the contribution of technical progress is the largest （32.04%）, followed by grain subsidies （8.55%）, the average monthly temperature （4.26%）, the average monthly precipitation （-0.88%）, the adjusted scale effect （-5.66%）, and growth in technical efficiency （-21.01%）. In general, the contribution of climate factors and agricultural policy factor are positive and significant.

Fully Coupled Forward-Backward Stochastic Functional Differential Equations and Applications to Quadratic Optimal Control

This paper considers the fully coupled forward-backward stochastic functional differential equations(FBSFDEs) with stochastic functional differential equations as the forward equations and the generalized anticipated backward stochastic differential equations as the backward equations. The authors will prove the existence and uniqueness theorem for FBSFDEs. As an application, we deal with a quadratic optimal control problem for functional stochastic systems, and get the explicit form of the optimal control by virtue of FBSFDEs.

Maximum principle for optimal control of neutral stochastic functional differential systems

This paper is concerned with optimal control of neutral stochastic functional differential equations(NSFDEs). The Pontryagin maximum principle is proved for optimal control, where the adjoint equation is a linear neutral backward stochastic functional equation of Volterra type(VNBSFE). The existence and uniqueness of the solution are proved for the general nonlinear VNBSFEs. Under the convexity assumption of the Hamiltonian function, a sufficient condition for the optimality is addressed as well.

STABILITY OF THE SOLUTIONS TO STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

In this paper,we obtain the stability of solutions to stochastic functional differential equations with infinite delay at phase space BC((-∞,0];Rd),under non-Lipschitz condition with Lipschitz condition being considered as a special case and a weakened linear growth condition by means of the corollary of Bihari inequality.

Non-densely defined impulsive neutral stochastic functional differential equations driven by fBm in Hilbert space with infinite delay

We study a class of non-densely defined impulsive neutral stochastic functional differential equations driven by an independent cylindrical fractional Brownian motion （fBm） with Hurst parameter H ∈ （1/2, 1） in the Hilbert space. We prove the existence and uniqueness of the integral solution for this kind of equations with the coefficients satisfying some non-Lipschitz conditions. The results are obtained by using the method of successive approximation.

Farm Production Growth in the Upper and Middle Parts of the Yellow River Basin,China,During 1980-1999

The impact of inputs on farm production growth was evaluated by analyzing the economic data of the upper and middle parts of the Yellow River basin, China for the period of 1980-1999. Descriptive statistics were employed to characterize the temporal trends and spatial patterns in farm production and five pertinent inputs of cultivated cropland, irrigation ratio, agricultural labor, machinery power and chemical fertilizer. Stochastic frontier production function was applied to quantify the dependence of the farm production on these inputs. The growth of farm production was decomposed to reflect the contributions by input growths and change in total factor productivity.. The change in total factor productivity was further decomposed into the changes in technology and in technical efficiency. The gross value of farm production in the region of study increased by 1.6 fold during 1980-1999. Among the five selected farm inputs, machinery power and chemical fertilizer increased by 1.8 and 2.8 fold, respectively. The increases in cultivated cropland, irrigated cropland, and agricultural labor were all less than 0.16 fold. The growth in the farm production was primarily contributed by the increase in the total factor productivity during 1980-1985, and by input growths after 1985. More than 80% of the contributions by input growths were attributed to the increased application of fertilizer and machinery. In the change of total factor productivity, the technology change dominated over the technical efficiency change in the study period except in the period of 1985-1990, implying that institution and investment played important roles in farm production growth. There was a decreasing trend in the technical efficiency in the region of study, indicating a potential to increase farm production by improving the technical efficiency in farm activities. Given the limited natural resources in the basin, the results of this study suggested that, for a sustainable growth of farm production in the area, efforts should be directed to technology progress and improvement in technical efficiency in the use of available resources.