The current PhD thesis investigates an important feature of some Monte Carlo algorithms - their complexity that depends on computation time and approximation error. In the PhD thesis several Monte Carlo algorithms for evaluating multidimensional integrals and for solving integral equations have been studied. Their computational complexity have been investigated and analysed. Some of these algorithms have been applied for solving real-life problems - investigation of electron energy distribution during electron-phonon interaction in semiconductors and providing sensitivity analysis of model output.
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