Numerical modeling of growth of multiplicative random quantities

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 $10^5$.