Stationary distribution for the Jacobi equation with a large random curvature parameter
Keywords:
stationary distribution, product of matrices, integral equation, Jacobi equationAbstract
A generalization of the results obtained previously for the case when the curvature parameter of the Jacobi equation is a random quantity distributed on a large or infinite interval is proposed. In this case the realization of the numerical algorithm for finding the stationary measure has some features compared to the previously introduced method. These features are mainly due to the finite numerical accuracy and are discussed in this paper together with the corresponding distributions. These distributions are used to calculate the Lyapunov exponent and the growth rate of statistical moments of the Jacobi field.
References
- Илларионов Е.А., Соколов Д.Д., Тутубалин В.Н. Стационарное распределение произведения матриц со случайными коэффициентами // Вычислительные методы и программирование. 2012. 13. 218-225.
- Bougerol P., Lacroix J. Product of random matrices with application to Schrödinger operators // Progress in Probability and Statistics. 1985. 8. 1-283.
- Comtet A., Texier C., Tourigny Y. Products of random matrices and generalized quantum point scatterers // Journal of Statistical Physics. 2010. 140. 427-466.
- Furstenberg H. Noncommuting random products // Trans. Amer. Math. Soc. 1963. 108. 377-428.
- Tutubalin V.N. A central limit theorem for products of random matrices and some of its applications // Symposia Mathematica. 1977. Т. XXI. 101-116.
- Zeldovich Ya.B., Ruzmaikin A.A., Molchanov S.A., Sokoloff D.D. Kinematic dynamo problem in a linear velocity field // J. Fluid Mech. 1984. 144. 1-11.
- Михайлов Е.А., Соколов Д.Д., Тутубалин В.Н. Фундаментальная матрица для уравнений Якоби со случайными коэффициентами // Вычислительные методы и программирование. 2010. 11. 261-268.
Downloads
Published
21-01-2013
How to Cite
Илларионов Е. Stationary Distribution for the Jacobi Equation With a Large Random Curvature Parameter // Numerical Methods and Programming (Vychislitel’nye Metody i Programmirovanie). 2013. 14. 38-43
Issue
Section
Section 1. Numerical methods and applications