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Using the stochastic approximation theory, a rigorous analysis of the convergence properties of the algorithm was presented.

然后，采用随机逼近理论，严格分析了算法的收敛性。

We show that the positive solution of the associated stochastic differential equation does not explode to infinity in a finite time.

文中给出了随机微分方程存在唯一正解，且解在有限时间内不爆破。

Both of them are the normal distance of the tangent plane at the check point on the limit state surface in the generalized stochastic space and the asymptotic formula for Laplace''s integral respectively.

提出了利用广义随机变量空间失效极限状态曲面上验算点处切平面法线和Laplace型积分渐近公式两种确定任意分布的荷载变量相关下结构的可靠指标的新方法，改进了现行防波堤失效概率计算理论。

Secondly, a asymptotic approximation formula of structurefailure probability is presented in generalized stochastic space with correlatedrandom variables by the asymptotic method of Laplace integral, by which the failureprobability and risk analysis on the chamfered vertical breakwater have been done.

其次，利用Laplace型积分的渐近计算方法，还推导出了广义随机空间相关荷载变量作用下结构失效概率的一个新的渐近计算公式，并依此算法对削角直立堤进行失效概率的计算以及风险评估。

Second, by studying the asymptotic behavior of the solution, we obtain the existence of random attractor for the stochastic quasi-geostrophic dynamical system.

另一方面，通过研究解的渐近行为，我们得到随机准地转动力系统的随机吸引子的存在性。

This paper discuss the asymptotic properties of several types of neutral stochastic functional differential equations.

本文讨论几种类型的中立型随机泛函微分方程解的渐近性质。

Stochastic Petri Nets has good ability for dynamic analysis of concurrency, asynchronism and uncertainty of systems. It is particularly suitable for system modeling and dependability analysis.

随机Petri网对系统的并发性、异步性和不确定性具有很强的动态分析能力，特别适合系统建模和可信赖性分析。

This paper proposes a non-linear adaptive filtering method based on analyzing the performance of the conventional adaptive methods in the cases of that the NBI can be modeled as a single tone,an autoregressive stochastic process or narrow band BPSK digital modulation signals.

在分析线性自适应滤波抑制单频干扰、自回归过程窄带干扰和窄带BPSK调制信号干扰的性能的基础上，提出了一种非线性自适应波抑制方法。

Finally, a stochastic averaging method based on generalized harmonic functions has been introduced and applied to the study of dynamics of Brownian particles.

最后，本文介绍了一种基于广义谐和函数的随机平均法，并将它初步应用于受宽带噪声激励下的Brown粒子随机运动系统的研究。

Finally, all the results obtained by using the stochastic averaging method for quasi-Hamiltonian system agree well with those obtained from digital simulation.

通过与数字模拟结果的比较，说明拟哈密顿系统的随机平均法可方便地应用于二自由度碰撞振动系统的预测并具有很好的精度。

Through comparing with the results by simulation to study the effects of theprojectile"s final velocity, the angle of rotation and the ballistic trajectory"s migration withdifferent projectile"s rotating speeds, different target"s moving speeds and differentpenetration angles.

通过比较数值模拟的结果来研究不同弹头转速、目标速度、侵彻角对侵彻过程中弹头最终速度、翻转角度和弹道偏移的影响。

I love stationery and all the accoutrement of writing.

我爱文具以及所有的书写的工具装备。