Chernoff Averages of Linear Differential Equations

Chernoff averages for random operator-valued functions generated by solutions of linear differential equations with variable coefficients on the real line are considered. Sufficient conditions are obtained for the convergence of the sequence of the Chernoff averages to a semigroup solving the Cauchy problem for the corresponding Fokker–Planck equation. The case of non-stationary random parameters is considered.