Agent-based Models with Stochastic Differential Equations in Systems Biology and Financial Economics
Date Issued
2009
Date
2009
Author(s)
Wang, Tse-Yi
Abstract
Biological networks and economic systems are complex stochastic systems. There are several particular approaches to deal with the complexity and stochasticity. But this field has become a battleground for two distinct methods: those employing statistical physics models tend to follow deductive approach, and those who do not use physics models favor inductive method of realist theory construction. In this dissertation, we propose a general combination methodology based on agent-based models, which is a variation of the statistical physics model, and stochastic differential equations. Starting with observation on the way systems change over time, the realist stochastic differential equations are inductively constructed for real-world prediction, and the artificial agent-based models are analogically simulated for in-silico experiments. The main result of this combination methodology exhibits that the artificial rules imposed on behaviors of in-silico agents deductively lead to the realist equations describing time-dependence of real-world mechanisms.o illustrate the methodology, two case studies are presented: one is to model gene regulatory networks in systems biology and the other is to predict stock indexes in financial economics. Both examples demonstrate that combining agent-based models with stochastic differential equations provides a more complete methodology for complex stochastic systems, and establishes a more solid linkage between in-silico experiments and real-world prediction.
Subjects
agent-based models
stochastic differential equations
complex systems
randomness
emergence
statistical physics
gene regulatory networks
stock markets
Type
thesis
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