Fundamental solutions, transition densities and the integration of Lie symmetries

Craddock, M

Fundamental solutions, transition densities and the integration of Lie symmetries

Craddock, M

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Publication Type:: Journal Article
Citation:: Journal of Differential Equations, 2009, 246 (6), pp. 2538 - 2560
Issue Date:: 2009-03-15

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Field	Value	Language
dc.contributor.author	Craddock, M	en_US
dc.date.issued	2009-03-15	en_US
dc.identifier.citation	Journal of Differential Equations, 2009, 246 (6), pp. 2538 - 2560	en_US
dc.identifier.issn	0022-0396	en_US
dc.identifier.uri	http://hdl.handle.net/10453/8263
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. © 2008 Elsevier Inc. All rights reserved.	en_US
dc.relation.ispartof	Journal of Differential Equations	en_US
dc.relation.isbasedon	10.1016/j.jde.2008.10.017	en_US
dc.subject.classification	General Mathematics	en_US
dc.title	Fundamental solutions, transition densities and the integration of Lie symmetries	en_US
dc.type	Journal Article
utslib.citation.volume	6	en_US
utslib.citation.volume	246	en_US
utslib.for	0102 Applied Mathematics	en_US
utslib.for	0101 Pure Mathematics	en_US
dc.location.activity	ISI:000264013600016	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	6	en_US
pubs.publication-status	Published	en_US
pubs.volume	246	en_US

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. © 2008 Elsevier Inc. All rights reserved.

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http://hdl.handle.net/10453/8263