Large deviation theory for stochastic difference equations
Large deviation theory for stochastic difference equations
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随机差分方程的大偏差理论
DOI：
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发表时间：
1997
影响因子：
1.9
通讯作者：
J. Keller
中科院分区：
文献类型：
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作者：
R. Kuske;J. Keller
考虑随机差分方程解 yn 的概率密度。继 Knessl 等人之后。 [1]，它被证明满足主方程，该方程对于指数 n 的大值是渐近求解的。该方法通过导出独立同分布随机变量之和以及两个相关和的联合密度的大偏差结果来说明。然后将其应用于随机介质中亥姆霍兹方程的差分近似。该方程解的衰减率的概率密度得到了较大的偏差结果。指数和指前因子均已确定。
The probability density for the solution yn of a stochastic difference equation is considered. Following Knessl et al. [1], it is shown to satisfy a master equation, which is solved asymptotically for large values of the index n. The method is illustrated by deriving the large deviation results for a sum of independent identically distributed random variables and for the joint density of two dependent sums. Then it is applied to a difference approximation to the Helmholtz equation in a random medium. A large deviation result is obtained for the probability density of the decay rate of a solution of this equation. Both the exponent and the pre-exponential factor are determined.