Random Processes in Physics and Finance

This text is aimed at professionals and students working on random processes in various areas, including physics and finance. The first author, Melvin Lax (1922-2002), was a distinguished Professor of Physics at City College of New York and a member of the U. S. National Academy of Sciences, widely known for his contribution on random processes in physics. Most chapters of this book are the outcome of the class notes which Lax taught at the City University of New York from 1985 to 2001. The material is unique as it presents the theoretical framework of Lax's treatment of random processes, starting from basic probability theory, to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanation of very narrow laser width and analytical solution of the elastic Boltzmann transport equation. Lax's critical viewpoint on mathematics currently used in the financial world is also presented in this book.1. Review of Probability ; 2. What is a random process ; 3. Examples of Markovian processes ; 4. Spectral measurement and correlation ; 5. Thermal noise ; 6. Shot noise ; 7. The fluctuation-dissipation theorem ; 8. Generalized Fokker-Planck equation ; 9. Langevin processes ; 10. Langevin treatment of the Fokker-Planck process ; 11. The rotating wave van del Pol oscillator (RWVP) ; 12. Noise in homogeneous semiconductors ; 13. Random walk of light in turbid media ; 14. Analytical solution of the elastic transport equation ; 15. Signal extraction in the presence of smoothing and noise ; 16. Stochastic methods in investment decision ; 17. Spectral analysis of economic time series