Stochastic Differential Equation Models with Time-Varying Parameters

Restricted (Penn State Only)
Author:
Chen, Meng
Graduate Program:
Human Development and Family Studies
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
July 05, 2017
Committee Members:
  • Sy-Miin Chow, Thesis Advisor
Keywords:
  • Stochastic Differential Equation
  • Time-varying Parameter
Abstract:
Self-organization occurs when a system shows distinct shifts in dynamics due to variations in the parameters that govern the system. Relatedly, many human dynamic processes with self-organizing features comprise subprocesses that unfold across multiple time scales. Incorporating time-varying parameters (TVPs) into a dynamic model of choice provides one way of representing self-organization as well as multi-time scale processes. Extant applications involving models with TVPs have been restricted to formulation in discrete time. Related work for representing time-varying parameters in continuous-time models remains scarce. We propose a stochastic differential equation (SDE) modeling framework with TVPs as a way to capture self-organization in continuous time. We present several examples of SDEs with TVPs, including a stochastic damped oscillator model with hypothesized functional shifts in both set-points and damping. Furthermore, we discuss plausible models that may be used to approximate changes in the TVPs in the absence of further knowledge concerning their true change mechanisms.