强连续半群的概率型逼近

Probabilistic Approximations for Strongly Continuous Semigrooups

借助于算子值数学期望以及概率论方法,得到了Banach空间上强连续半群的概率表示式,进而利用Taylor展开式、Holder不等式及适当的随机变量的矩生成函数估计式等工具,以较为简化的形式给出了强连续半群概率型逼近及收敛速度的估计式.

By means of operator-valued mathematical expectation and probabilistic methods, the probabilistic representations for strongly continuous semigroups on Banach space are obtained. Then, through Taylor expansion of the semigroup, Holder's inequality and estimations of moment-generating functions of some suitable random variables, some briefly probabilistic approximations and estimations of convergent rates are given for strongly continuous semigroups.