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Article

Lie Infinitesimal Conserved Quantities for Itô Stochastic ODEs

by
E. Fredericks
1,*,
F.M. Mahomed
2,* and
K. Masike
1
1
Mathematics and Applied Mathematics Bldg., Room 310.1, University of Cape Town, Rondebosch, 7700, South Africa
2
Centre for Differential Equations, Continuum Mechanics and Applications, School of Computational and Applied Mathematics, University of the Witwatersrand, Wits 2050, South Africa
*
Authors to whom correspondence should be addressed.
Math. Comput. Appl. 2010, 15(4), 601-612; https://doi.org/10.3390/mca15040601
Published: 1 December 2010
Versions Notes

Abstract

A methodology for constructing conserved quantities with Lie symmetry infinitesimals in an Itô integral context is pursued. The basis of this construction relies on Lie bracket relations on both the instantaneous drift and diffusion of an Itˆo stochastic ordinary differential equation (SODE).
Keywords: Lie infinitesimal; stochastic ordinary differential equation; conserved quantity Lie infinitesimal; stochastic ordinary differential equation; conserved quantity

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MDPI and ACS Style

Fredericks, E.; Mahomed, F.M.; Masike, K. Lie Infinitesimal Conserved Quantities for Itô Stochastic ODEs. Math. Comput. Appl. 2010, 15, 601-612. https://doi.org/10.3390/mca15040601

AMA Style

Fredericks E, Mahomed FM, Masike K. Lie Infinitesimal Conserved Quantities for Itô Stochastic ODEs. Mathematical and Computational Applications. 2010; 15(4):601-612. https://doi.org/10.3390/mca15040601

Chicago/Turabian Style

Fredericks, E., F.M. Mahomed, and K. Masike. 2010. "Lie Infinitesimal Conserved Quantities for Itô Stochastic ODEs" Mathematical and Computational Applications 15, no. 4: 601-612. https://doi.org/10.3390/mca15040601

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