| 二阶矩过程为n阶均方可导的一个充要条件 |
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| 引用本文： | 马强,戴朝寿,徐亚娟. 二阶矩过程为n阶均方可导的一个充要条件[J]. 徐州师范大学学报(自然科学版), 2005, 23(2): 44-47 |
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| 作者姓名： | 马强 戴朝寿 徐亚娟 |
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| 作者单位： | 1. 江苏技术师范学院,基础部,江苏,常州,213001;徐州师范大学,数学系,江苏,徐州,221116
2. 徐州师范大学,数学系,江苏,徐州,221116 |
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| 基金项目： | 徐州师范大学重点基金资助项目(04XLA01) |
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| 摘 要： | 一般的随机过程教材中只对一个二阶矩过程均方可导与其相关函数广义可导的等价性进行论述．将广义导数推广到n阶的情形，利用数学归纳法证明了二阶矩过程{X(t)，t∈R}为n阶均方可导与其相关函数n阶广义可导之间的等价性，并给出了判断二元函数f(s，t)为n阶广义可导的一个充分条件．
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| 关 键 词： | 二阶矩过程 可导 n阶 充要条件 相关函数 数学归纳法 广义导数 随机过程 二元函数 充分条件 等价性 |
| 文章编号： | 1007-6573(2005)02-0044-04 |
| 修稿时间： | 2005-01-11 |
A Necessary and Sufficient Condition of n-Order Mean Square Differentiability for a Second Moment Stochastic Process |
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| MA Qiang,DAI Chao-shou,XU Ya-juan. A Necessary and Sufficient Condition of n-Order Mean Square Differentiability for a Second Moment Stochastic Process[J]. Journal of Xuzhou Normal University(Natural Science Edition), 2005, 23(2): 44-47 |
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| Authors: | MA Qiang DAI Chao-shou XU Ya-juan |
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| Affiliation: | MA Qiang 1,2,DAI Chao-shou 2,XU Ya-juan 2 |
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| Abstract: | In general textbooks of stochastic process,only the equivalency between mean square differentiability of the process and generalized differentiability of the relevant function about a second moment stochastic process is expounded. In this paper, generalized derivative is extended to n-order case, and the equivalency between n-order mean square differentiability of the process and n-order generalized differentiability of relevant function is proved by means of mathematical induction. In addition, a sufficient condition judging n-order generalized differentiability for f(s,t) is given. |
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| Keywords: | second moment stochastic process n-order mean square differentiability n-order generalized differentiability |
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