Fundamental solutions, transition densities and the integration of Lie symmetries

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Show simple item record Craddock, Mark en_US
dc.contributor.editor en_US 2010-05-28T09:42:08Z 2010-05-28T09:42:08Z 2009 en_US
dc.identifier 2008007875 en_US
dc.identifier.citation Craddock Mark 2009, 'Fundamental solutions, transition densities and the integration of Lie symmetries', Academic Press Inc Elsevier Science, vol. 246, no. 6, pp. 2538-2560. en_US
dc.identifier.issn 0022-0396 en_US
dc.identifier.other C1 en_US
dc.description.abstract In this paper we present some new applications of Lie symmetry analysis to problems in stochastic calculus. The major focus is on using Lie symmetries of parabolic PDEs to obtain fundamental solutions and transition densities. The method we use relies upon the fact that Lie symmetries can be integrated with respect to the group parameter. We obtain new results which show that for PDEs with nontrivial Lie symmetry algebras, the Lie symmetries naturally yield Fourier and Laplace transforms of fundamental solutions, and we derive explicit formulas for such transforms in terms of the coefficients of the PDE. en_US
dc.language en_US
dc.publisher Academic Press Inc Elsevier Science en_US
dc.relation.hasversion Accepted manuscript version en_US
dc.relation.isbasedon en_US
dc.rights NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Differential Equations. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Differential Equations, VOL 246, ISSUE 6, (2009) DOI: en_US
dc.title Fundamental solutions, transition densities and the integration of Lie symmetries en_US
dc.parent Journal Of Differential Equations en_US
dc.journal.volume 246 en_US
dc.journal.number 6 en_US
dc.publocation San Diego en_US
dc.identifier.startpage 2538 en_US
dc.identifier.endpage 2560 en_US SCI.Faculty of Science en_US
dc.conference Verified OK en_US
dc.for 010200 en_US
dc.personcode 980626 en_US
dc.percentage 100 en_US Applied Mathematics en_US
dc.classification.type FOR-08 en_US
dc.edition en_US
dc.custom en_US en_US
dc.location.activity ISI:000264013600016 en_US
dc.description.keywords Lie symmetry groups; Fundamental solutions; Diffusion processes; Transition densities; Harmonic analysis en_US
dc.staffid en_US
dc.staffid 980626 en_US

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