Geodesic
Numerical modeling of growth of multiplicative random quantities
Numerical methods and programming, Tome 8 (2007) no. 1, pp. 1-5

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We present some results of numerical modeling for a simple ordinary differential equation with a random coefficient. We compare these results with the previous results obtained when modeling the Jacobi fields on a geodesic line on a manifold with a random curvature. We demonstrate a subexponential growth for the solution, while the solutions to the Jacobi equation grow exponentially. A progressive growth of statistical moments is demonstrated. The sample size sufficient for such a progressive growth is shown to be as large as $10^3$, while the size required for the Jacobi equation is about $10^5$.
Keywords: numerical simulation, equation with random coefficients, manifold with random curvature.
Mots-clés : Jacobi equation 
@article{VMP_2007_8_1_a0,
     author = {D. A. Grachev and D. D. Sokoloff},
     title = {Numerical modeling of growth of multiplicative random quantities},
     journal = {Numerical methods and programming},
     pages = {1--5},
     publisher = {mathdoc},
     volume = {8},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a0/}
}
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D. A. Grachev; D. D. Sokoloff. Numerical modeling of growth of multiplicative random quantities. Numerical methods and programming, Tome 8 (2007) no. 1, pp. 1-5. http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a0/