Fourier Analysis of Economic Phenomena
Fourier Analysis of Economic Phenomena (Monographs in Mathematical Economics)
by Toru Maruyama
English | 2018 | ISBN: 9811327297 | 413 Pages | PDF | 5.10 MB
by Toru Maruyama
English | 2018 | ISBN: 9811327297 | 413 Pages | PDF | 5.10 MB
Many economic theories have analyzed cyclical behaviors of economic variables. In this book, the focus is on a couple of trials: (1) the Kaldor theory and (2) the Slutsky effect. The Kaldor theory tries to explain business fluctuations in terms of nonlinear, 2nd-order ordinary differential equations (ODEs). In order to explain periodic behaviors of a solution, the Hopf-bifurcation theorem frequently plays a key role. Slutsky's idea is to look at the periodic movement as an overlapping effect of random shocks. The Slutsky process is a weakly stationary process, the periodic (or almost periodic) behavior of which can be analyzed by the Bochner theorem. The goal of this book is to give a comprehensive and rigorous justification of these ideas. Therefore, the aim is first to give a complete theory that supports the Hopf theorem and to prove the existence of periodic solutions of ODEs; and second to explain the mathematical structure of the Bochner theorem and its relation to periodic (or almost periodic) behaviors of weakly stationary processes.