title: A New Approach to the Series Expansion of Iterated Stratonovich Stochastic Integrals with Respect to Components of a Multidimensional Wiener Process. The Case of Arbitrary Complete Orthonormal Systems in Hilbert Space
metadata.name: dc.contributor.author
metadata.value: Kuznetsov, Dmitriy Feliksovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-12-02T15:37:39Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-12-02T15:37:39Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2024-06
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2024.206
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/48050
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article is devoted to the development of a new approach to the series expansion of iterated Stratonovich stochastic integrals with respect to components of a multidimensional Wiener process. This approach was proposed by the author in 2022 and is based on generalized multiple Fourier series in complete orthonormal systems of functions in Hilbert space. In the previous parts of this work, expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 6 were obtained. At that, the expansions were constructed using two specific bases in Hilbert space. More precisely, Legendre polynomials and the trigonometric Fourier basis were used. In this paper, expansions of iterated Stratonovich stochastic integrals of multiplicities 1 to 4 are obtained on the base of arbitrary complete orthonormal systems of functions in Hilbert space. Sufficient conditions for the expansion of iterated Stratonovich stochastic integrals of arbitrary multiplicity are formulated in terms of trace series. The results of the article will be useful for construction of strong numerical methods with orders 1.0, 1.5 and 2.0 (based on the Taylor-Stratonovich expansion) for Ito stochastic differential equations with non-commutative noise.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Differential Equations and Control Processes;Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: iterated Stratonovich stochastic integral
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: iterated Itô stochastic integral
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Itô stochastic differential equation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multidimensional Wiener process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: generalized multiple Fourier series
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mean-square convergence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: expansion
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A New Approach to the Series Expansion of Iterated Stratonovich Stochastic Integrals with Respect to Components of a Multidimensional Wiener Process. The Case of Arbitrary Complete Orthonormal Systems in Hilbert Space
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 24206-jdecp-kuznetsov-df.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/48050/1/24206-jdecp-kuznetsov-df.pdf
resources.format: Adobe PDF
resources.size: 713,33 kB