Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2018
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914330015956992 |
|---|---|
| author | Kuznetsov, Dmitriy F. |
| author_facet | Kuznetsov, Dmitriy F. |
| contents | The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the mean. We adapt this method for iterated Stratonovich stochastic integrals of multiplicity 3 from the Taylor-Stratonovich expansion. The main result of the article has been derived with using the triple Fourier-Legendre series and triple trigonometric Fourier series for the general case of series summation. Some recent results on the expansion of iterated Stratonovich stochastic integrals of multiplicities 3 to 6 are given. The results of the article can be applied to the numerical integration of Ito stochastic differential equations in accordance with the strong criterion of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_01564 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation Kuznetsov, Dmitriy F. Probability The article is devoted to the development of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series converging in the mean. We adapt this method for iterated Stratonovich stochastic integrals of multiplicity 3 from the Taylor-Stratonovich expansion. The main result of the article has been derived with using the triple Fourier-Legendre series and triple trigonometric Fourier series for the general case of series summation. Some recent results on the expansion of iterated Stratonovich stochastic integrals of multiplicities 3 to 6 are given. The results of the article can be applied to the numerical integration of Ito stochastic differential equations in accordance with the strong criterion of convergence. |
| title | Expansion of Iterated Stratonovich Stochastic Integrals of Multiplicity 3 Based on Generalized Multiple Fourier Series Converging in the Mean: General Case of Series Summation |
| topic | Probability |
| url | https://arxiv.org/abs/1801.01564 |