20.500.12556/RUL-119096 Naključni slonji sprehodi delo diplomskega seminarja Elephant random walks Obravnavamo naključni slonji sprehod, kjer so prirastki odvisni od celotne zgodovine procesa. Izračunamo funkciji pričakovane vrednosti in variance procesa ter ugotovimo, da naključni sprehod pri določeni vrednosti parametrov modela preide iz difuznega v superdifuzni režim. Obravnavamo konvergenco procesa in pokažemo, da zanj velja krepki zakon velikih števil. Ugotovimo, da v difuznem režimu in tudi na točki prehoda ustrezno normaliziran proces konvergira k normalni slučajni spremenljivki, v superdifuznem režimu pa k nedegenerirani slučajni spremenljivki, ki pa ni normalna. We consider the random elephant walk, where the increments depend on the whole history of the process. We calculate functions of expected value and variance of the process and see, that depending on the values of parameters, the process exhibits diffusive and superdiffusive behaviour. We discuss the convergence of the process and show, that the strong law of large numbers holds. In diffusive regime and also at the transition point, the process, when suitably normalized, converges to a normal random variable. However, this is not the case in superdiffusive regime, where we have convergence to a non-degenerate, yet not normal random variable. slučajni procesi naključni slonji sprehodi stohastična konvergenca difuzni režim superdifuzni režim mejna superdifuznost stochastic processes elephant random walks stochastic convergence diffusive regime superdiffusive regime marginal superdiffusion true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-03 08:15:02 2020-09-03 08:15:16 2024-05-30 10:07:18 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 519.2 108286 33313027 1366.pdf 1366.pdf 1 6F2D67571866F8E6813C7EB5785512D7 9c44401806b01cfafcb4aec1922936f4c691c657af3174d76ef5faf95dbd444a bb37e2d0-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=133752 1367.zip 1367.zip 1 19458DF05626EB08CD021F56560C59A6 dc48bf7a988b807c7c2aada5e8303fa847b9eb5967766037b6ae237e70d6f722 bb5ba138-a1b9-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=133754 Fakulteta za matematiko in fiziko 0 0 0