title: A New Proof of the Expansion of Iterated Ito Stochastic Integrals with Respect to the Components of a Multidimensional Wiener Process Based on Generalized Multiple Fourier Series and Hermite Polynomials
metadata.name: dc.contributor.author
metadata.value: Kuznetsov, Dmitriy Feliksovich
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2024-01-10T12:09:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2024-01-10T12:09:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2023-12
metadata.lang: -
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu35.2023.405
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/44574
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article is devoted to a new proof of the expansion for iterated Ito stochastic integrals with respect to the components of a multidimensional Wiener process. The above expansion is based on Hermite polynomials and generalized multiple Fourier series in arbitrary complete orthonormal systems of functions in a Hilbert space. In 2006, the author obtained a similar expansion, but with a lesser degree of generality, namely, for the case of continuous or piecewise continuous complete orthonornal systems of functions in a Hilbert space. In this article, the author generalizes the expansion of iterated Ito stochastic integrals obtained by him in 2006 to the case of an arbitrary complete orthonormal systems of functions in a Hilbert space using a new approach based on the Ito formula. The obtained expansion of iterated Ito stochastic integrals is useful for constructing of high-order strong numerical methods for systems of Ito stochastic differential equations with multidimensional 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 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: iterated Itô stochastic integral
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multiple Wiener 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: generalized multiple Fourier series
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multidimensional Wiener process
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Hermite polynomial
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mean-squareconvergence
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: expansion
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: A New Proof of the Expansion of Iterated Ito Stochastic Integrals with Respect to the Components of a Multidimensional Wiener Process Based on Generalized Multiple Fourier Series and Hermite Polynomials
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 67-124.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/44574/1/67-124.pdf
resources.format: Adobe PDF
resources.size: 379,56 kB