Ganychenko I. Rates of convergence in limit theorems for additive and multiplicative functionals

The accuracy rates of approximation of integral functionals with non-regular kernels of Markov processes are established for the quite wide types of processes under an assumption on the process formulated only in terms of its transition probability density. The rates of strong approximation for integral functionals of Markov processes by integral sums are obtained in the case of the bounded non-regular kernels of the integral functional. In the case where the kernels of the integral functionals satisfy an additional regularity assumption, deeper rates of strong approximation for the integral functionals of Markov processes are established. The rates of weak approximation for integral functionals of Markov processes by integral sums are established in the case of the bounded non-regular kernels of the integral functional. For a singular kernel of the integral functional, the accuracy rates of discrete approximation of the local time of a multidimensional diffusion process are obtained.