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.
Melvin Lax (Deceased) Distinguished Professor of Physics City College of New York Melvin Lax was a Distinguished Professor of Physics at the City College of the City University of New York (1971-2002), and a member of the U. S. National Academy of Sciences (1983-2002). He has been associated with Bell Laboratories as a member of the technical staff (1955-1972), as head of the Theoretical Physics Research Department (1962-1964) and as consultant to the Solid State Electronics Research Laboratory. After receiving his PhD in Physics from MIT (1947), Dr. Lax advanced from assistant to full professor of Physics at Syracuse University, (1947-55). He has also taught at Princeton (Spring 1961) and at Oxford (1961-1962). Dr. lax has published more than 200 papers. In 1999 Lax shared the Willis Lamb Medal for Laser Science and Quantum Optics. Dr. Lax was listed Who's Who in America. Wei Cai Senior research staff Institute for Ultrafast Spectroscopy and lasers Department of Physics City College of New York Wei Cai received Ph. D degree in Physics from University of Houston in 1985. He also received a MS degree in computer science from City College of City University of New York in 1992. He joined the Department of Physics at the City College of the City University of New York as a research associate in 1985. Recently, he is a senior member of the research staff at the Institute for Ultrafast Spectroscopy and Lasers. His main research interests are in radiative transfer and optical image processing. He has published 55 papers and holds 4 U. S. Patent. Min Xu Research staff Institute for Ultrafast Spectroscopy and lasers Department of Physics City College of New York Min Xu received Ph. D degree in Physics from City University of New York in 2001. He is currently a research associate at the Institute for Ultrafast Spectroscopy and Lasers. He works at the interface of physics, engineering and biomedical sciences. His main research interests are in optical physics, stochastic processes and inverse problems in physical and biological sciences, in particular, biomedical optical spectroscopy and imaging. He has published 30 peer-reviewed journal papers and holds 1 U. S. Patent.
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