| Home  | About ScienceAsia  | Publication charge  | Advertise with us  | Subscription for printed version  | Contact us  
Editorial Board
Journal Policy
Instructions for Authors
Online submission
Author Login
Reviewer Login
Volume 50 Number 5
Volume 50 Number 4
Volume 50 Number 3
Volume 50 Number 2
Volume 50 Number 1
Volume 49 Number 6
Earlier issues
Volume  Number 

previous article next article

Research articles

ScienceAsia 49S (2023):ID 59-67 |doi: 10.2306/scienceasia1513-1874.2023.s002


An application of solutions of linear difference equations for obtaining the conditional moments of the trending Ornstein-Uhlenbeck processes


Nopporn Thamrongrat, Kong Kanjanasopon, Sanae Rujivan*

 
ABSTRACT:     This paper presents an application of solutions of linear difference equations for obtaining a closed-form formula for the ?-th conditional moment of the Ornstein-Uhlenbeck (O-U) process, for any positive real number ?. The partial differential equation associated with the O-U process is reduced to a system of ordinary differential equations, which can be solved analytically in Laplace-transformed space using solutions of linear difference equations. Our success in performing Laplace inverse transform leads to a simple closed-form formula for the conditional moment. Interestingly, several asymptotic properties of the conditional moment can easily be deduced using our closed-form formula. Secondly, the n-th conditional moment of the trending O-U process is derived in closed form, for any positive integer n. Finally, we derive the n-th unconditional moment of the O-U process and explore some asymptotic properties.

Download PDF

20 Downloads 679 Views


a Center of Excellence in Data Science for Health Study, Division of Mathematics and Statistics, School of Science, Walailak University, Nakhon Si Thammarat 80161 Thailand

* Corresponding author, E-mail: rsanae@wu.ac.th

Received 17 Jan 2023, Accepted 17 Jul 2023