Itôv integral i primjene

Kovačević, Ana (2015) Itôv integral i primjene. Diploma thesis, Faculty of Science > Department of Mathematics.

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Abstract

In this paper we have constructed Itô integral that is defined as a limit of certain sequence of random variables. We have proved Itô formula which is analogous to Newton–Leibniz formula. Also, we have proved that Itô integral has martingale property. Combining the last two observations, we get a powerful tool for constructing martingales and inspecting whether a random variable is a martingale. Later in the thesis we have observed conformal invariance of Brownian motion. It states that, under conformal mapping, Brownian motion is mapped to another time changed Brownian motion. However, conformal invariance is not the only invariance property of Brownian motion. In the first chapter we have shown that Brownian motion is also invariant under scaling (with a time change). In the final chapter we have proved Feynman–Kac formula which gives the explicit formula of the solution to the heat equation.

Item Type: Thesis (Diploma thesis)
Supervisor: Mimica, Ante
Date: 2015
Number of Pages: 47
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 20 Oct 2015 11:18
Last Modified: 20 Oct 2015 11:18
URI: http://digre.pmf.unizg.hr/id/eprint/4150

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