This respected high-level text is aimed at students and professionals 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, and is widely known for his contributions to our understanding of random processes in physics. Most chapters of this book are outcomes 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, from basic probability theory to Fokker-Planck and Langevin Processes, and includes diverse applications, such as explanations of very narrow laser width, analytical solutions of the elastic Boltzmann transport equation, and a critical viewpoint of mathematics currently used in the world of finance.
`A rich selection of material, presented with insight and sophistication. ... full of wisdom, and rewarding for the expert.'
Michael Shlesinger, Office of Naval Research, Arlington, VA
`... clear and well organized, with effective pedagogy. An important book.'
Morrel Cohen, Rutgers University
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 of Markov Process
9: Langevin Process
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 Boltzmann Transport Equation
15: Signal Extraction in the Presence of Smoothing and Noise
16: Stochastic Methods to Investment Decision
17: Spectral Analysis of Economic Time Series