Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


30413.pdf (6.18 MB)

ETD Abstract Container

Abstract Header

A Study of Stochastic Processes in Natural and Social Sciences

Liu, Zhiyuan
http://rave.ohiolink.edu/etdc/view?acc_num=ucin153027399786377

Abstract Details

2018, PhD, University of Cincinnati, Arts and Sciences: Physics.
Bouchaud-Mezard network model and the combination of lognormal and Pareto distribution are two models that could give power-law tails. We applied these models to describe the distribution of human response time. We studied the scaling property of each model and used bootstrap method to obtain the confidence intervals of each shape related parameters. Then we studied the fundamental properties of the inverse Gamma stochastic process. We derived the relaxation time of the moments, the correlation function, and the relaxation time of the distribution. We find that the relaxation time of moments and correlation time of correlation function are characterized by the ratio of the coefficient of the drift part and square of the coefficient of the stochastic part. We also find that the distribution of the relaxation time of the distribution is inverse Gaussian. As to the Bouchaud-Mezard network model, we find that there is no steady state in a finite network because the average wealth changes with time. We also find that the distribution of the average wealth from different networks could be described by a lognormal distribution. At last, we studied one popular stock return model - Heston model. By using the product distribution and joint probability distribution function, we could get the distribution of the stock log-return in a short time, and it is consistent with results of the Heston model. We also applied the inverse Gamma process as the stochastic process of variance, and concluded that the Heston model was better.
Rostislav Serota, Ph.D. (Committee Chair)
F Paul Esposito, Ph.D. (Committee Member)
John Holden, Ph.D. (Committee Member)
Andrei Kogan, Ph.D. (Committee Member)
Michael Ma, Ph.D. (Committee Member)
102 p.
Physics

Recommended Citations

Citations

  • Liu, Z. (2018). A Study of Stochastic Processes in Natural and Social Sciences [Doctoral dissertation, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin153027399786377

    APA Style (7th edition)

  • Liu, Zhiyuan. A Study of Stochastic Processes in Natural and Social Sciences. 2018. University of Cincinnati, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin153027399786377.

    MLA Style (8th edition)

  • Liu, Zhiyuan. "A Study of Stochastic Processes in Natural and Social Sciences." Doctoral dissertation, University of Cincinnati, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin153027399786377

    Chicago Manual of Style (17th edition)

ucin153027399786377
247
© 2018, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.