Borel summation of the small time expansion of some SDE’s driven by Gaussian white noise

Albeverio, Sergio; Smii, Boubaker

doi:10.3233/asy-191525

Cited by 5 publications

(3 citation statements)

References 57 publications

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“…Our current focus lies at the crossroads of white noise analysis, Itô calculus, and algebraic quantum physics. While there is a very large prior literature in the area, we wish here to especially call attention to the following papers by Albeverio et al [1,2,3,4,5,6]. Some of the basic concepts that we study here can also be found, in special cases, and in one form or the other, with variants of our main themes, at [51,52,30,39].…”

Section: Introductionmentioning

confidence: 96%

White Noise Space Analysis and Multiplicative Change of Measures

Alpay,

Jorgensen,

Porat

2021

Preprint

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In this paper we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom.A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogues of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces, and Fock spaces. The latter forms the setting for our CCR representations. We further show, with the use of representation theory, and infinite-dimensional analysis, that our pairwise inequivalent probability spaces (for the Gaussian processes) correspond in an explicit manner to pairwise disjoint CCR representations. Contents 17 4.2. Generalized infinite Fourier transform 19 4.3. The canonical commutation relations 22 References 25

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Section: Introductionmentioning

confidence: 96%

White Noise Space Analysis and Multiplicative Change of Measures

Alpay,

Jorgensen,

Porat

2021

Preprint

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“…The dynamics of many phenomena studied in sciences, engineering and economy are described in many cases by stochastic differential equations (SDEs), see for example [1,2,6]. Stochastic partial differential equations (SPDE) is an interesting class of SDEs with numerous applications in different fields, which received a lot of attention during the last 50 years.…”

Section: Introductionmentioning

confidence: 99%

“…[3]. Asymptotic expansions of the solution of a class of SDEs or SPDEs are also studied in [4,6,7,25].…”

Section: Introductionmentioning

confidence: 99%

A Graphical Representation of the Truncated Moment of the Solution of a Nonlinear SPDE

Smii,

Kroumi

2023

Int. J. Anal. Appl.

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We consider a stochastic partial differential equation driven by a Lévy type noise (SPDE). Particular attention is given to the correlation function which measures the moments of the solution. Using the Feynman graph formalism, the solution of the SPDE as well as its truncated moments are given as a sum over specific graphs that are evaluated according to some rules. A remark on some applications will be given at the end of this work.

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White noise space analysis and multiplicative change of measures

Alpay

Jørgensen

Porat

2022

Journal of Mathematical Physics

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In this paper, we display a family of Gaussian processes, with explicit formulas and transforms. This is presented with the use of duality tools in such a way that the corresponding path-space measures are mutually singular. We make use of a corresponding family of representations of the canonical commutation relations (CCR) in an infinite number of degrees of freedom. A key feature of our construction is explicit formulas for associated transforms; these are infinite-dimensional analogs of Fourier transforms. Our framework is that of Gaussian Hilbert spaces, reproducing kernel Hilbert spaces and Fock spaces. The latter forms the setting for our CCR representations. We further show, with the use of representation theory and infinite-dimensional analysis, that our pairwise inequivalent probability spaces (for the Gaussian processes) correspond in an explicit manner to pairwise disjoint CCR representations.

show abstract

Borel summation of the small time expansion of some SDE’s driven by Gaussian white noise

Cited by 5 publications

References 57 publications

White Noise Space Analysis and Multiplicative Change of Measures

White Noise Space Analysis and Multiplicative Change of Measures

A Graphical Representation of the Truncated Moment of the Solution of a Nonlinear SPDE

White noise space analysis and multiplicative change of measures

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