Limit Theorems on Convergence to Generalized Cauchy Type Processes

We prove a limit theorem on convergence of mathematical expectations functionals sums independent random variables to Cauchy problem solution for an evolution equation $$ \frac{\partial u}{\partial t}={\left(-1\right)}^m{\mathcal{A}}_{\mu }, where {\mathcal{A}}_m is convolution operator with generalized function |x|−2m − 2, m ∈ N.