Fizikos bakalauras: KRAŠTINIŲ SĄLYGŲ ĮTAKA SAVIPANAŠIEMS PROCESAMS

Abstraktas: In this thesis, the influence of boundary conditions on self-similar processes is investigated. Self-similar processes, such as fractional Brownian motion (fBm) and Lévy $\alpha$-stable processes, are known for their long-range dependencies and self-similarity properties. The primary focus of this work is to understand how applying different boundary conditions, specifically elastic and inelastic, impacts the statistical properties of these processes. By generating realizations of fBm and Lévy $\alpha$-stable processes, and subsequently applying boundary conditions, the study aims to observe changes in their behavior and statistical characteristics. The research utilizes computational tools and methods to perform these simulations, emphasizing the importance of boundary conditions in accurately modeling physical phenomena. The findings from this study are expected to provide valuable insights for applications in various scientific fields, including physics, hydrology, and finance, where understanding the behavior of self-similar processes under constraints is crucial.

Keywords: fractional Brownian motion (fBm), Lévy $\alpha$-Stable Processes, Boundary Conditions, Self-Similar Processes, Statistical Properties, Computational Simulations, Elastic Boundaries, Inelastic Boundaries, Anomalous Diffusion, Hurst Exponent.

Plakatas pristatytas Open Readings konferencijoje (HurstSelfConsistency): https://www.overleaf.com/read/gstndxfbtgfq#42dc08

Skaidrės ir bakalauro Latex failas: https://www.overleaf.com/read/vjbwvpgqgfqs#0f3c24