o:2842 Numeričke metode Euler-ovog tipa za stohastičke diferencijalne jednačine sa kašnjenjem Numerical Euler-type methods for stohastic differental equations with delay : doctoral dissertation sr In general case, stochastic differential equations (SDEs) are not explicitly solvable, such tht studying numerical methods of approximation to their solutions is of great importance. The subject of the doctoral dissertation are numerical Euler-type methods for neutral SDEs with time-dependent delay (and Markovian switching). Most of the results are obtained assuming that the drift and diffusion coefficients of the considered equations grow superlinearly. The explicit numerical methods, such as the classical and truncated Euler-Maruyama (EM) methods, as well as semi-implicit Euler method, were sudied. Classes of equations for wich the explicit methods converge in the L p –sense for p ˃ 0 and order of L q-convergence of the truncated EM method for q ˃ 2 are determined. Beside the classes of equations for wich the classical and truncated EM methods converge, those for wich the mentioned methods diverge in a strong L p-sense on a finite time interval are also determined. Also, the L p-divergence of the semi-implicit Euler method for a class of neutral SDEs with time-dependent delay is proved. The techniques applied in proofs are influenced by the type of considered equation and the assumptions on its coefficients, as well as on the neutral term. Considerations are completed by examples and numerical simulations. Biografija: listovi 163-[164].Bibliografija: listovi 157-162. Datum odbrane: 06.12.2024. Stochastic analysis 91552100 160718857 91552101 8740 2025-03-18T11:43:50.053Z 45 no 46 Aleksandra, 1993- Petrović 121693449 2024 63 mentor Marija G. 1982- Milošević 15445607 2024 63 član komisije Miljana D., 1965- Jovanović 4019303 2024 63 član komisije Jasmina S., 1982- Đorđević 15444327 2024 63 član komisije Dušan D., 1991- Đorđević 80075529 2024 63 član komisije Ana, 1995 Merkle 121694217 2024 [7], 163 lista 3159363 http://phaidrani.ni.ac.rs/o:2842 no yes 12 2025-03-18T11:43:50.320Z 70 neutralne stohastičke diferencijalne jednačine, vremenski zavisno kašnjenje, proces Markova, L q-konvergencija, klasična i sečena metoda Ojler-Marujame, semiimplicitna Ojlerova metoda, uslov Hasminskog, L p-divergencija, superlinearni rast neutral stochastic differential equations, time-dependent delay, Markov process, L q-convergence, classical and truncated Euler-Maruyama methods, semi-implicit Euler method, Khasminskii condition, L p-divergence, super-linear growth 517.91:519.216(043.3) P 001 1738 18A07 18A0701 2024