Trapezoidal Stratified Monte Carlo Integration
Trapezoidal Stratified Monte Carlo Integration
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梯形分层蒙特卡罗积分
DOI：
10.1137/0729019
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发表时间：
1991
期刊：
影响因子：
--
通讯作者：
E. Masry
中科院分区：
文献类型：
--
作者：
S. Cambanis;E. Masry
随机过程的加权积分近似的梯形规则的基础上分层和对称的随机样本大小为n。权函数被假定为两次连续可微。被认为是收敛到零的均方积分逼近误差的样本容量无限增加的速度。对于二次均方连续可微的随机过程，证明了其速率为$n^{-5} $，正如没有随机分量一样[Math. Comp.，21（1967），pp. 388-397]。对于比一次多一点但不是两次的均方连续可微的随机过程，其速率为n^{ - 4} $。在这两种情况下，渐近常数也被确定。
Weighted integrals of random processes are approximated by the trapezoidal rule based on a stratified and symmetrized random sample of size n. The weight functions are assumed to be twice continuously differentiable. The rate of convergence to zero of the mean-square integral approximation error as the sample size increases indefinitely is considered. For random processes which are twice mean-square continuously differentiable, it is shown that the rate is $n^{ - 5} $, just as without a random component [Math. Comp., 21(1967), pp. 388–397]. For random processes which are a bit more than once, but not twice, mean-square continuously differentiable, the rate is shown to be $n^{ - 4} $. In both cases, the asymptotic constant is also determined.