离散时间Bernoulli噪声泛函上算子值函数的可微性

doi:10.6040/j.issn.1671-9352.0.2024.056

摘要/Abstract

摘要： 设M是具有混沌表示性质的离散时间正规鞅,S(M)⊂L²(M)⊂S^*(M)是与M相关的Gelfand三元组,用L(S(M),S^*(M))表示从S(M)到S^*(M)的连续线性算子构成的空间,O表示R^d的一个开集,探讨从O到L(S(M),S^*(M))的算子值函数的可微性。以2D-Fock变换为工具,得到从O到L(S(M),S^*(M))的算子值函数的可微性刻画定理。

关键词: 鞅, 2D-Fock变换, 卷积, 可微性

Abstract: Let M be a discrete-time normal martingale that has the chaotic representation property and S(M)⊂L2(M)⊂S^*(M) a Gelfand triple associated with M. Let L(S(M),S^*(M)) be the space of all continuous linear operators from S(M) to S^*(M) and O be an open subset of R^d. The differential of operator-valued functions from O to L(S(M),S^*(M)) is investigated. Mainly using the 2D-Fock transform as a tool, a differentiability characterization theorem is obtained for operator-valued functions from O to L(S(M),S^*(M)).

Key words: martingale, 2D-Fock transform, convolution, differentiability

中图分类号:

O177

唐玉玲. 离散时间Bernoulli噪声泛函上算子值函数的可微性[J]. 《山东大学学报(理学版)》, 2025, 60(9): 137-142.

TANG Yuling. Differentiability of operator-valued functions on discrete-time Bernoulli noise functionals[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(9): 137-142.

参考文献

[1] HUNG Zhiyuan, YAN Jiaan. Introduction to infinite dimensional stochastic analysis[M]. Dordrecht: Springer, 2000.
[2] OBATA N. Operator calculus on vector-valued white noise functionals[J]. Journal of Functional Analysis, 1994, 121(1):185-232.
[3] ITO Y. Generalized poisson functionals[J]. Probability Theory and Related Fields, 1988, 77(1):1-28.
[4] PRIVAULT N. Stochastic analysis of Bernoulli processes[J]. Probability Surveys, 2008, 5(1):435-483.
[5] NOURDIN I, PECCATI G, REINERT G. Steins method and stochastic analysis of rademacher functionals[J]. Electronic Journal of Probability, 2010, 15:1703-1742.
[6] POTTHOFF J. White noise approach to parabolic stochastic partial differential equation[J]. Stochastic Analysis and Application in Physics, 1994, 449:307-327.
[7] 王湘君,王才士. 广义算子值函数可微性的刻画[J]. 数学物理学报,2004,24(4):454-458. WANG Xiangjun, WANG Caishi. A characterized theorem of the differential of generalized operator-valued function[J]. Acta Mathematica Scientia, Series A, 2004, 24(4):454-458.
[8] WANG Caishi, CHAI Huifang, LU Yanchun. Discrete-time quantum Bernoulli noises[J]. Journal of Mathematical Physics, 2010, 51(5):1-8.
[9] WANG Caishi, CHEN Jinshu. Characterization theorems for generalized functionals of discrete-time normal martingale[J]. Journal of Function Spaces, 2015, 1:1-6.
[10] WANG Caishi, CHEN Jinshu. A characterization of operators on functionals of discrete-time normal martingales[J]. Stochastic Analysis and Applications, 2017, 35(2):305-316.
[11] 石佳,王才士,张丽霞,等. S^*(M)空间中的Bochner-Wick积分[J]. 山东大学学报(理学版),2020,55(6):23-31,40. SHI Jia, WANG Caishi, ZHANG Lixia, et al. Bochner-Wick integral for S^*(M) space[J]. Journal of Shandong University(Natural Science), 2020, 55(6):23-31,40.
[12] CHEN Jinshu. The Bochner-convolution integral for generalized functional-valued functions of discrete-time normal martingales[J]. Turkish Journal of Mathematics, 2020, 44(3):698-711.
[13] 陈金淑,唐玉玲. 离散时间正规鞅算子值函数的Bochner积分[J]. 应用概率统计,2023,39(3):436-448. CHEN Jinshu, TANG Yuling. Bochner integration of operator-valued functions in terms of discrete-time normal martingales[J]. Chinese Journal of Applied Probability and Statistics, 2023, 39(3):436-448.

相关文章 15

[1]	孔丽,李龙威,郝梦娇. 二十四面体金纳米颗粒的晶面调控与定量分析[J]. 《山东大学学报(理学版)》, 2025, 60(9): 1-9.
[2]	欧阳玉旋,彭垚潘,张荣芬,刘宇红. 改进高通道卷积的YOLOv7-tiny视觉辅助轻量化算法[J]. 《山东大学学报(理学版)》, 2025, 60(9): 62-70.
[3]	叶晓雅,王秀青,马海滨,张诺飞. EEG-MFNet:适用于脑电信号分析的轻量级多分支融合网络[J]. 《山东大学学报(理学版)》, 2025, 60(7): 1-12.
[4]	孙承杰,李宗蔚,单丽莉,林磊. 一种基于核心论元的篇章级事件抽取方法[J]. 《山东大学学报(理学版)》, 2024, 59(7): 53-63.
[5]	黎超,廖薇. 基于医疗知识驱动的中文疾病文本分类模型[J]. 《山东大学学报(理学版)》, 2024, 59(7): 122-130.
[6]	高玉峰,冯德成. 条件弱鞅和条件N-弱鞅的上(下)穿不等式[J]. 《山东大学学报(理学版)》, 2024, 59(6): 122-126.
[7]	赖华,张恒滔,线岩团,黄于欣. 融合分段编码与仿射机制的相似案例匹配方法[J]. 《山东大学学报(理学版)》, 2023, 58(1): 40-47.
[8]	鲁雅莉,冯德成,蔺霞. 弱鞅和N-弱鞅函数的一类极大值不等式[J]. 《山东大学学报(理学版)》, 2022, 57(10): 88-91.
[9]	冯德成,蔺霞,鲁雅莉. 基于cY函数的弱(下)鞅的一类极大值不等式[J]. 《山东大学学报(理学版)》, 2021, 56(11): 93-96.
[10]	阴爱英,林建洲,吴运兵,廖祥文. 融合图卷积神经网络的文本情感分类[J]. 《山东大学学报(理学版)》, 2021, 56(11): 15-23.
[11]	银温社,贺建峰. 基于深度学习的眼底图像出血点检测方法[J]. 《山东大学学报(理学版)》, 2020, 55(9): 62-71.
[12]	石佳,王才士,张丽霞,张银. S〓^*(M)空间中的Bochner-Wick积分[J]. 《山东大学学报(理学版)》, 2020, 55(6): 23-31.
[13]	李妮,关焕梅,杨飘,董文永. 基于BERT-IDCNN-CRF的中文命名实体识别方法[J]. 《山东大学学报(理学版)》, 2020, 55(1): 102-109.
[14]	刘洋,赵科军,葛连升,刘恒. 一种基于深度学习的快速DGA域名分类算法[J]. 《山东大学学报(理学版)》, 2019, 54(7): 106-112.
[15]	王文卿,撖奥洋,于立涛,张智晟. 自编码器与PSOA-CNN结合的短期负荷预测模型[J]. 《山东大学学报(理学版)》, 2019, 54(7): 50-56.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed