Transforms of RVs


Alternatives to the stochastic taylor expansion which is more trouble than it is worth.

Unscented transformm

(Roth, Hendeby, and Gustafsson 2016)

Collard, Fabrice, and Michel Juillard. 2001. “Accuracy of Stochastic Perturbation Methods: The Case of Asset Pricing Models.” Journal of Economic Dynamics and Control 25 (6-7): 979–99. https://ideas.repec.org/a/eee/dyncon/v25y2001i6-7p979-999.html.

Gustafsson, Fredrik, and Gustaf Hendeby. 2008. “On Nonlinear Transformations of Stochastic Variables and Its Application to Nonlinear Filtering.” In 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, 3617–20. https://doi.org/10.1109/ICASSP.2008.4518435.

———. 2012. “Some Relations Between Extended and Unscented Kalman Filters.” IEEE Transactions on Signal Processing 60 (2): 545–55. https://doi.org/10.1109/TSP.2011.2172431.

Hendeby, Gustaf, and Fredrik Gustafsson. 2007. “On Nonlinear Transformations of Gaussian Distributions,” 3. users.isy.liu.se/en/rt/fredrik/reports/07SSPut.pdf.

Jin, He-hui, Kenneth L Judd, and Hoover Insitution. n.d. “Perturbation Methods for General Dynamic Stochastic Models,” 44.

Kloeden, P. E., and E. Platen. 1991. “Stratonovich and Ito Stochastic Taylor Expansions.” Mathematische Nachrichten 151 (1): 33–50. https://doi.org/10.1002/mana.19911510103.

Kloeden, P. E., E. Platen, and I. W. Wright. 1992. “The Approximation of Multiple Stochastic Integrals.” Stochastic Analysis and Applications 10 (4): 431–41. https://doi.org/10.1080/07362999208809281.

Kloeden, Peter E., and Eckhard Platen. 1992. “Stochastic Taylor Expansions.” In Numerical Solution of Stochastic Differential Equations, edited by Peter E. Kloeden and Eckhard Platen, 161–226. Applications of Mathematics. Berlin, Heidelberg: Springer. https://doi.org/10.1007/978-3-662-12616-5_5.

———. 2010. Numerical Solution of Stochastic Differential Equations. Berlin, Heidelberg: Springer Berlin Heidelberg. https://public.ebookcentral.proquest.com/choice/publicfullrecord.aspx?p=3099793.

Roth, Michael, Gustaf Hendeby, and Fredrik Gustafsson. 2016. “Nonlinear Kalman Filters Explained: A Tutorial on Moment Computations and Sigma Point Methods” 11 (1): 24.

Schmitt-Grohe, Stephanie, and Martın Uribe. n.d. “Perturbation Methods for the Numerical Analysis of DSGE Models: Lecture Notes,” 38.

Schmitt-Grohé, Stephanie, and Martı́n Uribe. 2004. “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function.” Journal of Economic Dynamics and Control 28 (4): 755–75. https://doi.org/10.1016/S0165-1889(03)00043-5.