Solution of an abstract Cauchy problem with nonlinear and random perturbations in the Colombeau algebra

DOI10.1134/S106456241302021XzbMath1295.46029OpenAlexW2101397353MaRDI QIDQ2375972

Yanyan Li

Publication date: 25 June 2013

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s106456241302021x

zbMATH Keywords

white noiseColombeau algebrageneralised functionssemi-linear stochastic Cauchy problem

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) One-parameter semigroups and linear evolution equations (47D06) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (1)

Solution of quasilinear stochastic problems in abstract Colombeau algebras

Cites Work

• Kolmogorov equations for stochastic PDEs.
• Abstract stochastic equations. II: Solutions in spaces of abstract stochastic distributions.
• A model of white noise with values in a Hilbert space
• Regularized and generalized solutions of infinite-dimensional stochastic problems
• Peculiarities and regularization of ill-posed Cauchy problems with differential operators
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