Fundamental solutions, transition densities and the integration of Lie symmetries

DOI10.1016/j.jde.2008.10.017zbMath1227.35012OpenAlexW2009976632MaRDI QIDQ1011481

Mark Craddock

Publication date: 8 April 2009

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10453/8263

zbMATH Keywords

diffusion processesLie symmetry groups

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) PDEs with randomness, stochastic partial differential equations (35R60) Initial value problems for second-order parabolic equations (35K15) Solutions to PDEs in closed form (35C05) Stochastic analysis (60H99) Symmetries, invariants, etc. in context of PDEs (35B06)

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Cites Work

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• Lie group symmetries as integral transforms of fundamental solutions
• Fundamental solutions to Kolmogorov equations via reduction to canonical form
• On the equivalence of Lie symmetries and group representations
• The calculation of expectations for classes of diffusion processes by Lie symmetry methods
• The symmetry groups of linear partial differential equations and representation theory. I
• Symmetry groups of linear partial differential equations and representation theory: The Laplace and axially symmetric wave equation
• Symmetry group methods for fundamental solutions
• Symmetries and differential equations

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