Browsing by Author "Lennox, Kelly"

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Browsing by Author "Lennox, Kelly"

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  • Craddock, Mark; Lennox, Kelly (Inst Mathematical Statistics, 2009)
    This paper uses Lie symmetry methods to calculate certain expectations for a large class of Ito diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form ...
  • Craddock, Mark; Lennox, Kelly (Academic Press Inc Elsevier Science, 2007)
    We obtain fundamental solutions for PDEs of the form u(t) = sigma x(gamma)u(xx) + f(x)u(x) - mu x(r)u by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental ...
  • Craddock, Mark; Lennox, Kelly (Academic Press Inc Elsevier Science, 2012)
    In this paper we introduce new methods based upon integrating Lie symmetries for the construction of explicit fundamental solutions of multi-dimensional second order parabolic PDEs. We present applications to the problem ...
  • Craddock, Mark; Konstandatos, Otto; Lennox, Kelly (Nova Science Publishers, 2009)
    Lie group symmetry methods provide a powerful tool for the analysis of PDEs. Over the last thirty years, considerable progress has been made in the development of this field. In this article, we provide a brief introduction ...