Fundamental solutions, transition densities and the integration of Lie symmetries

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Show simple item record Craddock, MJ 2010-05-28T09:42:08Z 2009-01
dc.identifier.citation Journal Of Differential Equations, 2009, 246 (6), pp. 2538 - 2560
dc.identifier.issn 0022-0396
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.
dc.publisher Academic Press Inc Elsevier Science
dc.relation.hasversion Accepted manuscript version en_US
dc.relation.isbasedon 10.1016/j.jde.2008.10.017
dc.title Fundamental solutions, transition densities and the integration of Lie symmetries
dc.type Journal Article
dc.parent Journal Of Differential Equations
dc.journal.volume 6
dc.journal.volume 246
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 0102 Applied Mathematics
dc.personcode 980626
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.location.activity ISI:000264013600016
dc.description.keywords Lie symmetry groups
dc.description.keywords Fundamental solutions
dc.description.keywords Diffusion processes
dc.description.keywords Transition densities
dc.description.keywords Harmonic analysis
pubs.embargo.period Not known
pubs.organisational-group /University of Technology Sydney
pubs.organisational-group /University of Technology Sydney/Faculty of Science
pubs.organisational-group /University of Technology Sydney/Strength - Quantitative Finance
utslib.copyright.status Open Access 2015-04-15 12:23:47.074767+10
pubs.consider-herdc true
utslib.collection.history School of Mathematical Sciences (ID: 340)
utslib.collection.history General (ID: 2)

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