Lectures on Random Evolution
Lectures on Random Evolution
复制标题
随机进化讲座
DOI：
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发表时间：
1991
期刊：
影响因子：
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通讯作者：
M. Pinsky
中科院分区：
文献类型：
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作者：
M. Pinsky
随机进化是指一类随机过程，它按照一条随时间跳跃变化的规则进化。这与扩散过程相反，扩散过程假设规则随着时间不断变化。随机演化提供了一种非常灵活的语言，其优点是允许直接进行数值模拟--这对于扩散过程是不可能的。此外，它们还允许与双曲偏微分方程组和气体运动理论相联系，这在扩散过程的领域内是不可能的。它们还具有很大的几何不变性，允许在任意黎曼流形上进行公式化。在随机稳定性领域，随机演化提供了一些易于计算的模型来研究噪声影响下振子的Lyapunov指数和旋转次数。这本专著以一种易于理解和有趣的形式呈现了随机进化的各个方面，这将吸引大量的科学受众。
Random evolution denotes a class of stochastic processes which evolve according to a rule which varies in time according to jumps. This is in contrast to diffusion processes, which assume that the rule changes continuously with time. Random evolutions provide a very flexible language, having the advantage that they permit direct numerical simulation-which is not possible for a diffusion process. Furthermore, they allow connections with hyperbolic partial differential equations and the kinetic theory of gases, which is impossible within the domain of diffusion proceses. They also posses great geometric invariance, allowing formulation on an arbitrary Riemannian manifold. In the field of stochastic stability, random evolutions furnish some easily computable models in which to study the Lyapunov exponent and rotation numbers of oscillators under the influence of noise. This monograph presents the various aspects of random evolution in an accessible and interesting format which will appeal to a large scientific audience.