On an asymptotic representation of a normalizing factor for a random matrix-valued evolution (Q2771531)

Let \(\{N^{\varepsilon}(t),\varepsilon>0\}\) be a family of random matrix-valued evolutions constructed by a family of stochastically continuous nonnegative random processes depending on a small parameter. The author studies the asymptotic behaviour of the normalizing multiplier \(\rho^{\varepsilon}\) such that there is a finite limit as \(\varepsilon \to 0\) of the mathematical expectation \(EN^{\varepsilon}(\cdot)\) under the time scale parameter change \(t/\rho^{\varepsilon}\).