英文标题：
《Characterization of the Ito Integral》
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作者：
Lars Tyge Nielsen
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最新提交年份：
2018
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英文摘要：
  This paper provides an existence-and-uniqueness theorem characterizing the stochastic integral with respect to a Wiener process. The integral is represented as a mapping from the space of measurable and adapted pathwise locally integrable processes to the space of continuous adapted processes. It is characterized in terms of two properties: (1) how the stochastic integrals of simple processes are calculated and (2) how these integrals converge in probability when the time integrals of the squared integrands converge in probability.
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中文摘要：
本文给出了一个关于维纳过程的随机积分的存在唯一性定理。积分表示为从可测和自适应的路径局部可积过程空间到连续自适应过程空间的映射。它具有两个性质：（1）如何计算简单过程的随机积分；（2）当平方被积函数的时间积分以概率收敛时，这些积分如何以概率收敛。
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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：Quantitative Finance        数量金融学
二级分类：Mathematical Finance        数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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