Random hermite polynomials and Girsanov identities on the Wiener space

Privault N.

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Random hermite polynomials and Girsanov identities on the Wiener space

机译：Wiener空间上的随机Hermite多项式和Girsanov恒等式

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摘要

In this paper, we derive a formula for the expectation of random Hermite polynomials in Skorohod integrals, extending classical results in the adapted case. As an application we recover, under simple conditions and with short proofs, the anticipative Girsanov identity and quasi-invariance results obtained in Ref. 6 for quasi-nilpotent shifts on the Wiener space.

机译：在本文中，我们导出了Skorohod积分中的随机Hermite多项式期望的公式，并在适应的情况下扩展了经典结果。作为应用程序，我们可以在简单的条件下并以简短的证明来恢复参考文献中获得的预期Girsanov身份和准不变结果。维纳空间上的准幂零移位为6。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2010年第4期|共13页
作者
Privault N.;
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正文语种 eng
中图分类物理学;
关键词
Euclidean motions; Girsanov identity; Malliavin calculus; quasi-invariance; Skorohod integral; Wiener measure;

机译：欧氏运动;Girsanov身份;Malliavin演算;拟不变性;Skorohod积分;维纳测度;

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专利

1. Random hermite polynomials and Girsanov identities on the Wiener space [J] . Privault N. Infinite dimensional analysis, quantum probability, and related topics . 2010,第4期

机译：Wiener空间上的随机Hermite多项式和Girsanov恒等式
2. Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform [J] . Radha R., Thangavelu S. Journal of Mathematical Analysis and Applications . 2009,第2期

机译：全纯Sobolev空间，Hermite和特殊Hermite半群以及加窗傅立叶变换的Paley-Wiener定理
3. Deriving new identities of Hermite-polynomial operators and Laguerre-polynomial operators by using representation theory and operator-ordering technique [J] . Zhou J., Fan H.-Y., Song J. Optik: Zeitschrift fur Licht- und Elektronenoptik: = Journal for Light-and Electronoptic . 2013,第10期

机译：利用表示论和算子排序技术推导Hermite多项式算子和Laguerre多项式算子的新身份
4. Spaces of Analytic Functions Having Representations by Series of Hermite Polynomials [C] . G. I. Balikov, I. P. Dimitrov International Conference on Applications of Mathematics in Engineering and Economics . 2007

机译：分析函数的空间，其具有默认的Hermite多项式的表示
5. Derandomizing Isolation and Polynomial Identity Testing [D] . Prakriya Venkata, Subramanya Gautam. 2019

机译：去随机化隔离和多项式身份测试
6. Some symmetric identities for the generalized Bernoulli Euler and Genocchi polynomials associated with Hermite polynomials [O] . Waseem A. Khan, Hiba Haroon -1

机译：与Hermite多项式相关的广义BernoulliEuler和Genocchi多项式的一些对称恒等式
7. Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley–Wiener theorem for the windowed Fourier transform [O] . Radha R., Thangavelu S. 2009

机译：全纯Sobolev空间，Hermite和特殊Hermite半群以及开窗傅立叶变换的Paley-Wiener定理

Random hermite polynomials and Girsanov identities on the Wiener space

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