The calculation of expectations for classes of diffusion processes by lie symmetry methods

Publication Type:
Journal Article
Citation:
Annals of Applied Probability, 2009, 19 (1), pp. 127 - 157
Issue Date:
2009-02-01
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This paper uses Lie symmetry methods to calculate certain expectations for a large class of Itô diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form Ex(e-λxt-∫t0 g(Xs)ds) can be reduced to evaluating a single integral of known functions. Given a drift f we determine the functions g for which the corresponding functional can be calculated by symmetry. Conversely, given g, we can determine precisely those drifts f for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method. © Institute of Mathematical Statistics, 2009.
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