This book contains comprehensive descriptions of stochastic processes described by underdamped and overdamped oscillator equations with additive and multiplicative random forcing. The latter is associated with random frequency or random damping. The coverage includes descriptions of various new phenomena discovered in the last hundred years since the explanation of Brownian motion by Einstein, Smoluchovski and Langevin, such as the shift of stable points, noise-enhanced stability, stochastic resonance, resonant activation, and stabilization of metastable states. In addition to many applications in physics, chemistry, biology, medicine, economics and sociology, these discoveries have clarified the deep relationship between determinism and stochasticity, which turns out to be complimentary rather than contradictory, with noise playing both constructive and destructive roles.

Contents:

• Deterministic and Random Oscillators
• White and Colored Noise
• Brownian Motion
• Overdamped Harmonic Oscillator with Additive Noise
• Overdamped Harmonic Oscillator with Multiplicative Noise
• Overdamped Single-Well Oscillator
• Overdamped Double-Well Oscillator
• Harmonic Oscillator with Additive Noise
• Nonlinear Oscillator with Additive Noise
• Harmonic Oscillator with Random Frequency
• Harmonic Oscillator with Random Damping
• Nonlinear Oscillator with Multiplicative Noise

"This book makes for pleasant reading and can be warmly recommended to graduate students and to investigators of a wide range of subjects, from physical sciences to social sciences and technology."

"This book contains an excellent presentation by the author of topics of interest in the form of an expository survey article ... the author is well qualified to write this book. Finally, this is a short but interesting book for researchers interested in a research and seminar lecture presentation."