On Explicit Probability Laws for Classes of Scalar Diffusions

Mark Craddock and Eckhard Platen ()
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Mark Craddock: Department of Mathematical Sciences, University of Technology, Sydney

No 246, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper uses Lie symmetry group methods to obtain transition probability densities for scalar diffusions, where the diffusion coefficient is given by a power law. We will show that if the drift of the diffusion satisfies a certain family of Riccati equations, then it is possible to compute a generalized Laplace transform of the transition density for the process. Various explicit examples are provided. We also obtain fundamental solutions of the Kolmogorov forward equation for diffusions, which do not correspond to transition probability densities.

Keywords: Lie symmetry groups; fundamental solutions; transition probability densities, It?o diffusions (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2009-03-01

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