| Issue |
MATEC Web of Conferences
Volume 362, 2022
XXII International Conference on Computational Mechanics and Modern Applied Software Systems (CMMASS 2021)
|
|
|---|---|---|
| Article Number | 01027 | |
| Number of page(s) | 6 | |
| DOI | https://doi.org/10.1051/matecconf/202236201027 | |
| Published online | 14 September 2022 | |
Spectral representation of stochastic integration operators
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, 125993, Russia
* e-mail: rkoffice@mail.ru
The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in the form of a composition of spectral characteristics used in the spectral form of mathematical description for control systems. This spectral representation can be defined relative to the various orthonormal bases. For given deterministic square-integrable kernels, the spectral characteristic of a stochastic integration operator is determined as an infinite random matrix. The main applications of such a representation suppose solving linear stochastic differential equations and modeling multiple or iterated Stratonovich stochastic integrals. Specific formulas are provided that allow to represent the spectral characteristic for the stochastic integration operator, the kernel of which is the Heaviside function, relative to Walsh functions and trigonometric functions.
© The Authors, published by EDP Sciences, 2022
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