The Noisy Oscillator: The First Hundred Years, From Einstein Until Now

This book is an overview of the gamut of stochastic processes described by underdamped and overdamped oscillator equations with additive and multiplicative random forcing. What it lacks in depth it makes up for in breadth by covering this spectrum without rigorous mathematical proofs or statement. The result is a slim compendium that is a good and complete starting point for engineers and researchers needing to work in this area.

The arrangement is chronological. After preliminaries outlaying the foundation equations of this area of dynamical systems the book begins with the explanation of Brownian motion by Einstein, Smoluchovski and Langevin and continues on to advances as recent as 2004.

A focus of this text is the deep relationship between determinism and stochasticity, which turns out to be complementary rather than contradictory, with noise playing both constructive and destructive roles. Specific topics covered include white and colored noise, additive noise, multiplicative noise, random damping and more.

Tom Schulte is working his own random process at Oakland University picking a course here and a course there, winding his way toward a Masters Degree in mathematics.