本文对抛物型方程初——边值阿题给出了概率数值解法及误差分布的估计.方法是作维纳过程 W(s)参数集的一个分划,随机模拟过程 W(s)的 N 条轨迹在分划点的数值,理论上抽取方程解的概率表达式中关于维纳过程的随机微分方程的解——过程(Ma...本文对抛物型方程初——边值阿题给出了概率数值解法及误差分布的估计.方法是作维纳过程 W(s)参数集的一个分划,随机模拟过程 W(s)的 N 条轨迹在分划点的数值,理论上抽取方程解的概率表达式中关于维纳过程的随机微分方程的解——过程(Markov)ξ(s)中的 N 条轨迹,利用 Monto-carlo 方法及维纳过程在分划点的数值离散解的概率表达式,然后估计了误差分布的期望与方差。展开更多
Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger...Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.展开更多
文摘本文对抛物型方程初——边值阿题给出了概率数值解法及误差分布的估计.方法是作维纳过程 W(s)参数集的一个分划,随机模拟过程 W(s)的 N 条轨迹在分划点的数值,理论上抽取方程解的概率表达式中关于维纳过程的随机微分方程的解——过程(Markov)ξ(s)中的 N 条轨迹,利用 Monto-carlo 方法及维纳过程在分划点的数值离散解的概率表达式,然后估计了误差分布的期望与方差。
文摘Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.
