Spectral representation of stochastic integration operators
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...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2022-01-01
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| Series: | MATEC Web of Conferences |
| Online Access: | https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01027.pdf |
| _version_ | 1818017315124412416 |
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| author | Rybakov Konstantin |
| author_facet | Rybakov Konstantin |
| author_sort | Rybakov Konstantin |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T07:25:32Z |
| format | Article |
| id | doaj.art-8a00a438dcad4dd98adb5d618a9a4645 |
| institution | Directory Open Access Journal |
| issn | 2261-236X |
| language | English |
| last_indexed | 2024-04-14T07:25:32Z |
| publishDate | 2022-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | MATEC Web of Conferences |
| spelling | doaj.art-8a00a438dcad4dd98adb5d618a9a46452022-12-22T02:06:01ZengEDP SciencesMATEC Web of Conferences2261-236X2022-01-013620102710.1051/matecconf/202236201027matecconf_cmmass2021_01027Spectral representation of stochastic integration operatorsRybakov Konstantin0Moscow Aviation Institute (National Research University)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.https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01027.pdf |
| spellingShingle | Rybakov Konstantin Spectral representation of stochastic integration operators MATEC Web of Conferences |
| title | Spectral representation of stochastic integration operators |
| title_full | Spectral representation of stochastic integration operators |
| title_fullStr | Spectral representation of stochastic integration operators |
| title_full_unstemmed | Spectral representation of stochastic integration operators |
| title_short | Spectral representation of stochastic integration operators |
| title_sort | spectral representation of stochastic integration operators |
| url | https://www.matec-conferences.org/articles/matecconf/pdf/2022/09/matecconf_cmmass2021_01027.pdf |
| work_keys_str_mv | AT rybakovkonstantin spectralrepresentationofstochasticintegrationoperators |