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Large deviations for the local time of a jump diffusion with two sided reflections

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Large deviations for the local time of a jump diffusion with two sided reflections

Zoroddu, Giovanni (2018) Large deviations for the local time of a jump diffusion with two sided reflections. Masters thesis, Concordia University.

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Abstract

Let X be a jump diffusion, then its reflection at the boundaries 0 and b > 0 forms the process V . The amount by which V must reflect to stay within its boundaries is added to a process called the local time. This thesis establishes a large deviation principle for the local time of a reflected jump diffusion. Upon generalizing the notion of the local time to an additive functional, we establish the desired result through a Markov process argument. By applying Ito’s formula to a suitably chosen process M and in proving that M is a martingale, we find its associated integro-differential equation. M can then be used to find the limiting behavior of the cumulant generating function which allows the large deviation principle to be established by means of the Gartner-Ellis theorem. These theoretical results are then illustrated with two specific examples. We first find analytical results for these
examples and then test them in a Monte Carlo simulation study and by numerically solving the integro-differential equation.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Zoroddu, Giovanni
Institution:Concordia University
Degree Name:M.A.
Program:Mathematics
Date:31 August 2018
Thesis Supervisor(s):Popovic, Lea
Keywords:Large Deviations, Local Time, Reflected Jump Diffusion
ID Code:984325
Deposited By: GIOVANNI ZORODDU
Deposited On:16 Nov 2018 15:23
Last Modified:16 Sep 2019 18:42
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