An explicit Euler scheme for generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si11.svg" display="inline" id="d1e87"><mml:mi>n</mml:mi></mml:math>-dimensional second-order differential equations with initial value conditions driven by additive Gaussian white noises

Ranjbar, Hassan

doi:10.1016/j.cam.2024.116179

Journal of Computational and Applied Mathematics

2025

DOI: 10.1016/j.cam.2024.116179

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An explicit Euler scheme for generalized n-dimensional second-order differential equations with initial value conditions driven by additive Gaussian white noises

Hassan Ranjbar

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S-Contractive Mappings on Vector-Valued White Noise Functional Space and Their Applications

Ma,

Gong,

Wei

2024

Symmetry

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In this paper, we propose a new notion, which we name S-contractive mapping, in a framework of vector-valued white noise functionals Wω⊗N⊂Γ(H)⊗K⊂(Wω⊗N)*. And we give concrete definitions of S-contractive mappings for vector-valued white noise functionals. We establish the fixed-point theorems of S-contractive mappings. As applications, by applying the fixed-point theorems of generalized S-contractive mappings, we prove the existence and uniqueness of a generalized form of differential equations of vector-valued white noise functionals with weak conditions and investigate Wick-type differential equations of vector-valued white noise functionals with generalized conditions.

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S-Contractive Mappings on Vector-Valued White Noise Functional Space and Their Applications

Ma,

Gong,

Wei

2024

Symmetry

View full text Add to dashboard Cite

show abstract

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An explicit Euler scheme for generalized n-dimensional second-order differential equations with initial value conditions driven by additive Gaussian white noises

Cited by 1 publication

References 21 publications

S-Contractive Mappings on Vector-Valued White Noise Functional Space and Their Applications

S-Contractive Mappings on Vector-Valued White Noise Functional Space and Their Applications

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