Transformations of Wiener measure and orthogonal expansions

Dorogovtsev Andrey A.; Riabov Georgii

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Transformations of Wiener measure and orthogonal expansions

机译：维纳测度的变换和正交展开

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In this paper we study the structure of square integrable functionals measurable with respect to coalescing stochastic flows. The case of the Wiener process stopped at the moment of hitting an irregular continuous level is considered. Relying on the change of measure technique, we present a new construction of multiple stochastic integrals with respect to stopped Wiener process. An intrinsic analogue of the Ito-Wiener expansion for the space of square integrable functionals measurable with respect to the stopped Wiener process is constructed.

机译：在本文中，我们研究了关于可合并随机流可测量的平方可积泛函的结构。考虑到在达到不规则连续水平时维纳过程停止的情况。依靠测量技术的变化，相对于停止的维纳过程，我们提出了一种多元随机积分的新结构。构造了一个伊藤-维纳展开式的内在类似物，该展开式相对于停止的维纳过程可测量的平方可积函数的空间。

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《Infinite dimensional analysis, quantum probability, and related topics》 |2016年第3期|共18页
作者
Dorogovtsev Andrey A.; Riabov Georgii;
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正文语种 eng
中图分类物理学;
关键词
Wiener measure; chaos expansion; coalescence; stochastic flows;

机译：维纳测度;混沌扩展;聚结;随机流量;

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1. Transformations of Wiener measure and orthogonal expansions [J] . Dorogovtsev Andrey A., Riabov Georgii Infinite dimensional analysis, quantum probability, and related topics . 2016,第3期

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2. Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations [J] . Bandt Christoph, Barnsley Michael, Hegland Markus, Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2016,第Null期

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4. Relationship Of Time-domain And Frequency-domain Generalized Orthogonal Functional Expansions To Wiener Kernels [C] . Victor, J.D. Engineering in Medicine and Biology Society, 1990., Proceedings of the Twelfth Annual International Conference of the IEEE . 1990

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Transformations of Wiener measure and orthogonal expansions

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