随机的

Based on the equivalent transformation from fuzzy possibility distribution to random probability density distribution, the fuzzy random failure probability calculation can be formulated easily, and a First Order and Second Moment method for fuzzy - random analysis is established.

提出了模糊随机可靠性分析的近似解析和数字模拟综合方法，基于模糊变量的等价随机化变换，可以方便地得到模糊随机失效概率的计算公式，并建立了模糊随机可靠性分析的一次二阶矩法。

A two dimensional stochastic nonlinear dynamical model of semi-active suspension system is presented considering the stochastic factor of the road. The Hamilton function is also described as one dimension diffusion process by using stochastic average method, the stationary stability is studied by solving the Fokker-Planck-Kolmogorov equation. The Backward Kolmogorov equation for reliability function had been established.

考虑路面随机因素的影响，首先建立二自由度汽车半主动悬架的随机非线性动力学模型，运用随机平均法，将Hamilton函数表示为一维扩散过程，并运用奇异边界理论分析系统的全局随机稳定性，建立可靠性函数所满足的Backward Kolmogorov方程，结合初始条件和边界条件得出数值结果。

In essence, stream cipher is such a pseudorandom generator that its chaos sequence of output and random sequence are computational indistinguishability; and the aim in designing block cipher materially is to design a pseudorandom permutation which is computationally indistinguishable from random permutations.

实际上，序列密码本质上就是一个伪随机生成器G，其输出的乱数序列和随机序列是计算不可分辨的；而分组密码的设计目标实质上就是设计一个伪随机置换，它与随机置换是计算不可分辨的。

Fri particular, the Wittmann-type strong law of larg numbers for independent random variables is generalized to the case of NA random variables. We also present the sufficient and necessary condition of the laws of logarithm, and we extend Teicher-type strong law of the large numbers for sequence of NA random variables. Some of the laws of iterated logarithm of Teicher-type, Egorov-type arid Wittmann-type for sequence of NA random variables are obtained. Then we investigate the rate3f ionvergcll( fbr series of NA randonl variables, we obtain soIne results fbr tl1e Iaws of theiterated logarithttl, the laws of logarithm and decreasing order fOr the tail sum.Risk itllttlysis tlleory is a sigIlifica11t part of insurance InatheInatics.

Wittmann（1985a）关于实独立随机变量列的结果，并给出了NA列强大数律成立的若干条件，特别建立了一般NA列对数律成立的充分必要条件，在二阶矩存在的条件下完整的解决了一般NA列对数律的问题，中文摘要2而已有的一些NA列对数律的结果可以由它推出，给出了NA列的Teiclier型强大数律，表明lbiChCI·（1979）给出的实独立随机变量列的强大数律可以减弱其条件等；建立厂不问分布NA列的Teicfl仪；Egorov，Petrov型有界重对数律，以及加权同分布NA列的有界重对数律，进一步推广了NA列的Kolmogory有界重对数律等，特别对NA列建立了Wittm洲型有界重对数律，而其证明方法与独立情形有很大不同，同时通过反例表明在与独立场合类似的条件下，独立列的Wittmann有界重对数律不能完美的推广到NA歹小惰形；最后研究了NA随机变量级数的收敛速度，给出了尾和下降的阶；尾和的有界重对数律，及尾和对数律成立的充要条件等，并通过反例说明 NA随机变量级数与独立随机变量级数在收敛速度方面存在的差异。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

As a result, the mass matrix, the stiffness matrix, the damping matrix and the excitation coefficient matrices of the dynamics differential equations are random parameter matrices. According to the minimum deviation rule of the mean squares between the random parameter system and the deterministic parameter system, the random mean square deviation vector function between the two systems has been set up and the deterministic parameter system has been solved.

应用Newton-Euler矢量法对挂接车辆系统建立了质量阵、刚度阵、阻尼阵和激励系数阵皆为随机参数阵的八自由度随机参数系统动力学微分方程，并按照随机参数系统与确定性参数系统之间的均方值偏差最小的原则，建立了两系统之间的随机均方偏差矢量函数，由此解出了相应的确定性参数系统

Based on Bellman stochastic nonlinear dynamic programming, we develop an optimal control algorithm for the discrete stochastic system with conditional Markov structure.

基于Bellman随机非线性动态规划法，提出了具有条件马尔科夫跳变结构的离散随机系统的最优控制方法，应用随机变结构系统的性质对最优控制算法进行了简化处理，并将后验概率密度函数用条件高斯函数来逼近，针对一类具有条件马尔科夫跳变结构的线性离散随机系统，给出了其逼近最优控制算法。

Structural reliability usually is analyzed in Descartes coordinates in which the correlated random variables should be converted to uncorrelated random variables by an orthogonal transformation method.

针对正交空间内，对相关随机变量的可靠指标求解时，需要做正交变换的缺点，研究了广义随机空间内结构可靠指标的计算方法，首次提出了广义随机空间内结构可靠指标计算的随机有限元法。

Next, the existence of random fixed point for random semiclosed 1-set-contractive operator is discussed.

同时我们证明了重要的随机锐角原理、随机满射定理和随机一一映射定理。

Martingales, optimal stopping, Wald's lemma, age-dependent branching processes, stochastic integration, Ito's lemma.

随机过程：随机过程：鞅，最优停步，Wald 引理，依赖年龄的分支过程，随机积分， Ito 引理。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。