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Importance sample algorithm for rare event simulation of jump-diffusions based on Hamilton-Jacobi equations

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Importance sample algorithm for rare event simulation of jump-diffusions based on Hamilton-Jacobi equations

Guillen Cuevas, Alvaro (2017) Importance sample algorithm for rare event simulation of jump-diffusions based on Hamilton-Jacobi equations. Masters thesis, Concordia University.

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Abstract

Consider a marked point process or a jump-diffusion, from which we want to simulate a trajectory of the process or a functional of it. In both cases the magnitude of noise contributors is controlled by a small parameter epsilon. Raw Monte Carlo methods produce estimators with a large relative error, which increases even more as N increases or epsilon decreases. Using viscosity sub-solutions of Hamilton-Jacobi equations, we were able to produce importance sampling algorithms with optimal asymptotic behaviour and low relative error across a variety of small values of noise contribution. Some basic stochastic knowledge and means to produce the discretization of a trajectory of the jump-diffusion are needed, both of which are provided in this text. Furthermore, we applied the algorithm we developed to model the bistability in the concentration of certain molecular species.

Divisions:Concordia University > Faculty of Arts and Science > Mathematics and Statistics
Item Type:Thesis (Masters)
Authors:Guillen Cuevas, Alvaro
Institution:Concordia University
Degree Name:M. Sc.
Program:Mathematics
Date:August 2017
Thesis Supervisor(s):Popovic, Lea
ID Code:982900
Deposited By: ALVARO GUILLEN CUEVAS
Deposited On:16 Nov 2017 17:35
Last Modified:18 Jan 2018 17:56
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