The calculation of expectations for classes of diffusion processes by Lie symmetry methods
By Mark Craddock, K. Lennox. 2009
57 citations recorded by the source corpus.
This paper uses Lie symmetry methods to calculate certain expectations for a large class of It\^{o} diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form $E_x(e^{-\lambda X_t-\int_0^tg(X_s) ds})$ 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.
Subfields: Mathematical Physics, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/08d4243d00378c00f8b0df89b20d5d24fbb779b5
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Mathematical Physics
In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- Asymptotic Behavior of the Maximum Likelihood Estimator for Ergodic and Nonergodic Square-Root Diffusions (2013, methodology): “For this purpose, we use once again the recent work of [3].”