Κατεύθυνση Στατιστική και Επιχειρησιακή Έρευνα
Library of the School of Science

2015-09-09

2015

Ανδριόπουλος Γεώργιος

Χελιώτης Δημήτριος Επίκ. Καθηγητής (Επιβλέπων), Λουλάκης Μιχαήλ Επίκ. Καθηγητής , Παπανικολάου Βασίλειος Καθηγητής

Η Στοχαστική Εξίσωση Θερμότητας και το Συνεχές Τυχαίο Πολυμερές

Greek

The Stochastic Heat Equation and the Contnuum Random Polymer

This thesis presents important elements of the theory of Stochastic Partial
Differential Equations. It also presents the construction of a particular
random model through the analysis of the solutions of the stochastic heat
equation and their properties. In Chapter 1 we introduce the KPZ equation. More
specifically we focus on its connection with the stochastic heat equation. In
Chapter 2 we construct the stochastic integrals we use throughout this thesis.
In Chapter 3 we discuss the multiple versions of these integrals. In the next
chapters we discuss the stochastic heat equation in a rigorous way and in
Chapter 4we prove the existence of mild solutions. In Chapter 5 we present a
Large Deviations result which combined with a comparison theorem results in the
proof of the positivity of the solutions of the stochastic heat equation. In
conclusion, in Chapter 5 we construct the continuum random polymer, we prove
many of its properties and we write down the stochastic equation which
satisfies.

Stochastic, Heat, Continuum, Random, Polymer

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https://pergamos.lib.uoa.gr/uoa/dl/object/1317850