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摘要翻译：
我们在可能无限维状态空间上构造了实值函数的可控增长赋范空间，使得正有界算子$(P_t)_{T\ge0}$在其上具有$\lim_{T\to0+}P_tf(x)=f(x)$的半群实际上是强连续的。这一结果适用于证明具有线性增长特征的随机（偏）微分方程和具有控制增长特征的函数集的分裂格式的最优收敛速度。应用一般的Da Prato-Zabczyk型方程和利率理论中的HJM方程。
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英文标题：
《A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial)
Differential Equations》
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作者：
Philipp Doersek, Josef Teichmann
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最新提交年份：
2010
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分类信息：
一级分类：Mathematics 数学
二级分类：Probability 概率
分类描述：Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory
概率论与随机过程的理论与应用：例如中心极限定理，大偏差，随机微分方程，统计力学模型，排队论
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一级分类：Mathematics 数学
二级分类：Numerical Analysis 数值分析
分类描述：Numerical algorithms for problems in analysis and algebra, scientific computation
分析和代数问题的数值算法，科学计算
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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英文摘要：
We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon with $\lim_{t\to 0+}P_t f(x)=f(x)$ are in fact strongly continuous. This result applies to prove optimal rates of convergence of splitting schemes for stochastic (partial) differential equations with linearly growing characteristics and for sets of functions with controlled growth. Applications are general Da Prato-Zabczyk type equations and the HJM equations from interest rate theory.
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PDF链接：
https://arxiv.org/pdf/1011.2651
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