Prerokova neenakost : delo diplomskega seminarja

Markon, Tin (author), Bernik, Janez (mentor)

V okviru diplomskega seminarja sem preučil prerokovo neenakost in jo dokazal na podlagi dveh različnih ustavljalnih pravil. Dodatno, sem preko tretjega dokaza opisal, kako bi lahko generalizirali dokaz posebnega primera prerokove neenakosti, ko lahko izbiramo več slučajnih spremenljivk in raziskal primer ko so spremenljivke enakomerno omejene. Na koncu sem pripravil simulacijo s programskim jezikom Python in opisal uporabo prerokove neenakosti v praksi, natančneje pri uporabi mehanizmov dražb.

• Language: Slovenian
• Keywords: prerokova neenakost, optimalni časi ustavljanja, slučajni proces
• Work type: Final seminar paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2025
• PID: 20.500.12556/RUL-169322
• UDC: 519.2
• COBISS.SI-ID: 236942595
• Publication date in RUL: 23.05.2025

Secondary language

• Language: English
• Title: Prophet inequality

Abstract

As part of this diploma seminar, I have studied and provided proofs of the prophet inequality based on two different stopping rules. Additionally, by presenting a third proof, I described how one could generalize the special case of the prophet inequality when selecting multiple random variables and investigated the scenario of uniformly bounded random variables. Finally, I implemented a simulation in Python and discussed practical applications of the prophet inequality, specifically in the context of auctions.

• Keywords: prophet inequality, optimal stopping, random process