o:1802 Aproksimacije rešenja stohastičkih diferencijalnih jednačina primenom Taylor-ovih redova The Approximations of solutions to stochastic differential equations by applying Taylor series : doctoral dissertation sr The subject of the doctoral dissertation is the application of the Taylor formula for the coefficients of various types of stochastic differential equations, for the purpose of the approximation of theirs solutions under non standard conditions, such as the global Lipschitz condition and the linear growth condition. Under certain assumptions, the almost sure convergence and the convergence in the p-th mean, p>0, of the sequence of approximate solutions towards the solution of the initial equation, is shown. The rate of the Lp convergence increases as the orders of the Taylor approximations of the coefficients of the initial equation increase. Shown results are illustrated through the examples which are designed such that the global Lipschitz condition and/or the linear growth condition for the drift and diffusion coefficients are not satisfied. That way, the need for the shown results is satisfied. Techniques used in the proofs are determined by the type of the considered equation, as well as by the conditions which are assumed for the coefficients of the equations. Bibliografija: str. 111-116;Biobibliografski podaci: str. [117-118]. Datum odbrane: 17.12.2021. Stochastic analysis 91552100 57006345 91552101 8534 2022-11-24T18:59:01.053Z 45 no 46 Dušan D., 1991- Đorđević 80075529 2021 63 mentor Miljana D., 1965- Jovanović 4019303 2021 63 predsednik komisije Stevan Pilipović 2021 63 član komisije Marija Milošević 2021 63 član komisije Marija Krstić 2021 V, 116 str. 3346251 http://phaidrani.ni.ac.rs/o:1802 no yes 12 2022-11-24T18:59:01.320Z 70 Lp konvergencija, polinomijalni uslov, skoro izvesna konvergencija, stohastičke diferencijalne jednačine, stohastičke diferencijalne jednačine sa vremenski zavisnim kašnjenjem, funkcionalne stohastičke diferencijalne jednačine, neutralne stohastičke diferencijalne jednačine sa vremenskim kašnjenjem, Tejlorova aproksimacija, Frešeov izvod Lp convergence, polynomial condition, almost sure convergence, stochastic differential equations, stochastic differential equations with time dependent delay, stochastic functional differential equations, neutral stochastic differential equations with time related delay, Taylor approximation, Frechet derivative 519.216:517.9(043.3) P130 1738 18A07 18A0701 2021