一类带扰动的随机脉冲泛函微分方程解的渐近性北大核心CSCD

该文讨论了一类带扰动的随机脉冲泛函微分方程解的渐近性.通过比较扰动方程的解和原方程的解,得到了两者逼近的充分条件.首先,两者在有限的时间区间上相互逼近;其次,当扰动趋于零时,区间长度趋于无穷大,在这个区间上两个解仍然是相互逼近的.最后,举例说明了结果的有效性.     

求解张量随机互补问题的光滑牛顿算法

近年来, 越来越多的人意识到随机互补问题在经济管理中具有十分重要的作用。有学者已将随机互补问题由矩阵推广到张量, 并提出了张量随机互补问题。本文通过引入一类光滑函数, 提出了求解张量随机互补问题的一种光滑牛顿算法, 并证明了算法的全局和局部收敛性, 最后通过数值实验验证了算法的有效性。     

非对称碰撞约束下形状记忆合金梁的随机响应与分岔

形状记忆合金(SMA)是二十一世纪具有形状记忆效应的新型智能材料.针对具有非对称约束的SMA梁,本文构造了碰撞振动系统.在无碰撞和有碰撞两种情况下,利用随机平均法给出了近似解析结果.数值模拟作为验证解析结果的工具.结果表明,系统能量的概率响应曲线具有非光滑特性.当约束位置发生变化时,系统会出现随机P分岔和D分岔.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

A stream tube model for miscible flow

A simple theoretical model is described for deriving a 1-dimensional equation for the spreading of a tracer in a steady flow at the field scale. The originality of the model is to use a stochastic appoach not in the 3-dimensional space but in the 1-D space of the stream tubes. The simplicity of calculation comes from the local relationship between permeability and velocity in a 1-D flow. The spreading of a tracer front is due to local variations in the cross-sectional area of the stream tubes, which induces randomness in travel time. The derived transport equation is averaged in the main flow direction. It differs from the standard dispersion equation. The roles of time and space variables are exchanged. This result can be explained by using the statistical theory of Continuous Time Random Walk instead of a standard Random Walk. However, the two equations are very close, since their solutions have the same first and second moments. Dispersivity is found to be equal to the product of the correlation length by the variance of the logarithm of permeability, a result similar to Gelhar's macrodispersion.Nomenclature A total cross-section area of the sample - C (resident) concentration of tracer - D,D ^* dispersion coefficient - F flux of tracer - G probability distribution function for permeability in the stream-tube segments - I tracer intensity (mass crossing a surface per unit time) - K permeability - L length of the medium - M number of stream tubes in the medium - N number of segments along a stream tube - P pressure - Q total flow rate in the sample - a length of an elementary stream-tube segment - g probability distribution function for permeability in the space - i, j indices, tube numbers - q flow rate in each stream tube - s variable cross-section area of a stream tube - t, t time - u front velocity - x space variable in the flow direction - small local variation in time - , _t longitudinal, transverse dispersivity - porosity of the porous medium - correlation length in the permeability field - viscosity of the fluid - time for filling an elementary stream tube segment - standard deviation of a stochastic variable - probability distribution of arrival times (Gaussian)     

Stability of multistage stochastic programming

In this paper, we study the stability of multistage stochastic programming with recourse in a way that is different from that used in studying stability of two-stage stochastic programs. Here, we transform the multistage programs into mathematical programs in the space ⁿ ×L _p with a simple objective function and multistage stochastic constraints. By investigating the continuity of the multistage multifunction defined by the multistage stochastic constraints and applying epi-convergence theory we obtain stability results for linear and linear-quadratic multistage stochastic programs.Project supported by the National Natural Science Foundation of China.     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

Generalized solutions of a stochastic partial differential equation

We discuss the Cauchy problem of a certain stochastic parabolic partial differential equation arising in the nonlinear filtering theory, where the initial data and the nonhomogeneous noise term of the equation are given by Schwartz distributions. The generalized (distributional) solution is represented by a partial (conditional) generalized expectation ofT(t)° _0,t ^–1 , whereT(t) is a stochastic process with values in distributions and _s,t is a stochastic flow generated by a certain stochastic differential equation. The representation is used for getting estimates of the solution with respect to Sobolev norms.Further, by applying the partial Malliavin calculus of Kusuoka-Stroock, we show that any generalized solution is aC -function under a condition similar to Hörmander's hypoellipticity condition.     

Rate conservation laws: A survey

We survey the rate conservation law, RCL for short, arising in queues and related stochastic models. RCL was recognized as one of the fundamental principles to get relationships between time and embedded averages such as the extended Little's formulaH=G, but we show that it has other applications. For example, RCL is one of the important techniques for deriving equilibrium equations for stochastic processes. It is shown that the various techniques, including Mecke's formula for a stationary random measure, can be formulated as RCL. For this purpose, we start with a new definition of the rate with respect to a random measure, and generalize RCL by using it. We further introduce the notion of quasi-expectation, which is a certain extension of the ordinary expectation, and derive RCL applicable to the sample average results. It means that the sample average formulas such asH=G can be obtained as the stationary RCL in the quasi-expectation framework. We also survey several extensions of RCL and discuss examples. Throughout the paper, we would like to emphasize how results can be easily obtained by using a simple principle, RCL.     

Exact results for the asymmetric simple exclusion process with a blockage

We present new results for the current as a function of transmission rate in the one-dimensional totally asymmetric simple exclusion process (TASEP) with a blockage that lowers the jump rate at one site from one tor<1. Exact finitevolume results serve to bound the allowed values for the current in the infinite system. This proves the existence of a nonequilibrium phase transition, corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state. A series expansion inr, derived from the finite systems, is proven to be asymptotic for all sufficiently large systems. Padé approximants based on this series, which make specific assumptions about the nature of the singularity atr=1, match numerical data for the infinite system to 1 part in 10⁴.