Preface by Masanao Aoki

Summary

In the last ten years or so, I have devoted my research efforts to revising the commonly adopted frameworks for modeling and analysis by mainstream macroeconomists. Results of my initial thoughts and proposals were published in 1996, followed by another book in 2002. In these two books I explained my proposed methods for modeling and analyzing stochastic dynamic interactions among economic agents of possibly many different types, and how to analyze aggregate behavior and associated fluctuations. The two books are mostly exposition of concepts and techniques and had only a few suggestive economic examples.

I have realized that more substantive examples are needed to convince mainstream macroeconomists of the usefulness of my approaches. This book, jointly written with Hiroshi Yoshikawa, integrates the methodologies and approaches in these two earlier books with much more detailed analysis of more substantive and substantial macroeconomic examples.

As the subtitle of the book makes clear, our approaches have two components: (1) continuous-time Markov chains to model stochastic dynamic interactions among agents and (2) combinations of stochastic processes and non-classical combinatorial analysis, called combinatorial stochastic processes.

In (1) a version of Chapman–Kolmogorov equations called master equations describes how states of the models evolve stochastically over time. In this sense this part is devoted to applications of some of the concepts and methods from statistical physics.