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Inference based on boundary crossing of diffusions

Yi, Bowen/ B (2018) Inference based on boundary crossing of diffusions. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Nowadays, the boundary crossing problem of diffusion processes is of interest to both mathematicians and statisticians. In this thesis, we review the literature on the first passage time problem for both one-dimensional and two-dimensional diffusion processes. Then we investigate the statistical inference problem about unknown parameters of the Cox-Ingersoll-Ross model based on discretely observed first passage times. We are able to determine the identifiable parameter set, discuss the tail property of the density function in a neighborhood of the true parameter, and propose a conditional version of maximum likelihood estimation. We also list future work, including extensions of this problem to a general one-dimensional time homogeneous diffusion process, and to some special two-dimensional diffusion processes.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Yi, Bowen/ Bboy9@pitt.eduboy9
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairIyengar, Satishssi@pitt.edu
Committee MemberChadam, Johnchadam@pitt.edu
Committee MemberCheng, Yuyucheng@pitt.edu
Committee MemberRen, Zhaozren@pitt.edu
Date: 26 September 2018
Date Type: Publication
Defense Date: 23 July 2018
Approval Date: 26 September 2018
Submission Date: 1 August 2018
Access Restriction: 1 year -- Restrict access to University of Pittsburgh for a period of 1 year.
Number of Pages: 89
Institution: University of Pittsburgh
Schools and Programs: Dietrich School of Arts and Sciences > Statistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: First passage time, Cox-Ingersoll-Ross model, Maximum likelihood estimation
Date Deposited: 26 Sep 2018 23:21
Last Modified: 26 Sep 2018 23:21
URI: http://d-scholarship.pitt.edu/id/eprint/35083

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