Naključni slonji sprehodi

delo diplomskega seminarja

Enej Kovač (Author), Janez Bernik (Mentor)

Abstract

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.

Keywords

finančna matematika;slučajni procesi;naključni slonji sprehodi;stohastična konvergenca;difuzni režim;superdifuzni režim;mejna superdifuznost;

Data

Language:	Slovenian
Year of publishing:	2020
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[E. Kovač]
UDC:	519.2
COBISS:	33313027
Views:	1558
Downloads:	355
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Elephant random walks
Secondary abstract:	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.
Secondary keywords:	stochastic processes;elephant random walks;stochastic convergence;diffusive regime;superdiffusive regime;marginal superdiffusion;
Type (COBISS):	Final seminar paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Finančna matematika - 1. stopnja
Pages:	34 str.
ID:	12023814