The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 19, Number 1 (2009), 127-157.
The calculation of expectations for classes of diffusion processes by Lie symmetry methods
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−∫0tg(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.
Ann. Appl. Probab., Volume 19, Number 1 (2009), 127-157.
First available in Project Euclid: 20 February 2009
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35C05: Solutions in closed form 35K15: Initial value problems for second-order parabolic equations 60H99: None of the above, but in this section 60G99: None of the above, but in this section
Craddock, Mark; Lennox, Kelly A. The calculation of expectations for classes of diffusion processes by Lie symmetry methods. Ann. Appl. Probab. 19 (2009), no. 1, 127--157. doi:10.1214/08-AAP534. https://projecteuclid.org/euclid.aoap/1235140335